Calculus of Variations and Partial Differential Equations

Article	Citations
Non-polynomial entire solutions to Hessian equations	61
Compactness of certain class of singular minimal hypersurfaces	58
$$W^{\sigma ,p}$$ A priori estimates for fully nonlinear integro-differential equations	29
Min–max minimal hypersurfaces with obstacle	29
Dichotomous concentrating solutions for a Schrödinger–Newton equation	29
Harnack inequality and principal eigentheory for general infinity Laplacian operators with gradient in $$\mathbb {R}^N$$ and applications	28
A new transportation distance with bulk/interface interactions and flux penalization	25
Global well-posedness of 3D homogeneous and inhomogeneous MHD system with small unidirectional derivative	24
Optimal solutions for a class of set-valued evolution problems	24
Convergence rates for linear elasticity systems on perforated domains	23
Regularity for quasi-minima of the Alt–Caffarelli functional	21
Global vanishing viscosity limit for the two dimensional incompressible viscoelasticity in Lagrangian coordinates	20
Energy identity and necklessness for $$\alpha $$-Dirac-harmonic maps into a sphere	20
An extension of a theorem of Bers and Finn on the removability of isolated singularities to the Euler–Lagrange equations related to general linear growth problems	20
Strict convexity and $$C^1$$ regularity of solutions to generated Jacobian equations in dimension two	19
Generalized Brezis–Seeger–Van Schaftingen–Yung formulae and their applications in ball Banach Sobolev spaces	18
Multiple solutions of the planar $$L_p$$ dual Minkowski problem	18
Nonrelativistic limit and some properties of solutions for nonlinear Dirac equations	18
On the spectrum of a mixed-type operator with applications to rotating wave solutions	17
Bourgain–Brezis–Mironescu–Maz’ya–Shaposhnikova limit formulae for fractional Sobolev spaces via interpolation and extrapolation	17
Energy minimizers for an asymptotic MEMS model with heterogeneous dielectric properties	17
Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem	16
On the cauchy problem of 3D compressible, viscous, heat-conductive navier-stokes-Poisson equations subject to large and non-flat doping profile	15
Upper bounds for the Steklov eigenvalues on trees	15
Quadratically pinched hypersurfaces of the sphere via mean curvature flow with surgery	15

On the lower bound of the principal eigenvalue of a nonlinear operator	15
A Lichnerowicz-type estimate for Steklov eigenvalues on graphs and its rigidity	15
Perturbative estimates for the one-phase Stefan problem	14
Convergence rate of hypersonic similarity for steady potential flows over two-dimensional Lipschitz wedge	14
On the weak Harnack estimate for nonlocal equations	14
On the structure of minimizers of the Allen-Cahn energy for $$Z_N$$ symmetric nonnegative potentials with $$N+1$$ zeros	14
Partial regularity for Lipschitz solutions to the minimal surface system	14
Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities	13
Serrin–type regularity criteria for the 3D MHD equations via one velocity component and one magnetic component	13
A theory of spectral partitions of metric graphs	13
Gauss curvature flow with an obstacle	13
Local uniqueness of ground states for the generalized Choquard equation	12
On a theorem by Schlenk	12
Dynamics of nearly parallel vortex filaments for the Gross–Pitaevskii equation	12
Torus-like solutions for the Landau-de Gennes model. Part III: torus vs split minimizers	12
Generic existence of multiplicity-1 minmax minimal hypersurfaces via Allen–Cahn	12
Existence and orbital stability/instability of standing waves with prescribed mass for the $$L^{2}$$-supercritical NLS in bounded domains and exterior domains	12
Vanishing-concentration-compactness alternative for critical Sobolev embedding with a general integrand in $$\mathbb R^2$$	12
A new class of discrete conformal structures on surfaces with boundary	11
Gradient estimates for singular parabolic p-Laplace type equations with measure data	11
A continuum model for brittle nanowires derived from an atomistic description by $$\Gamma $$-convergence	11
Dynamical (In)Stability of Ricci-flat ALE metrics along the Ricci flow	11
Gamma-convergence of a nonlocal perimeter arising in adversarial machine learning	11
Asymptotic behavior of least energy nodal solutions for biharmonic Lane–Emden problems in dimension four	11
The optimal Hölder exponent in Massari’s regularity theorem	11
Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas	11
A flow approach to mean field equation	11
Nonlinear Schrödinger systems with trapping potentials for mixed attractive and repulsive interactions	11
Sobolev and Hölder regularity results for some singular nonhomogeneous quasilinear problems	11
Hermitian Yang–Mills connections on pullback bundles	10
First and second derivative Hölder estimates for generated Jacobian equations	10
Improved regularity for the parabolic normalized p-Laplace equation	10
Nonlinear bound states with prescribed angular momentum	10
Existence of minimizers and convergence of critical points for a new Landau-de Gennes energy functional in nematic liquid crystals	10
Up to the boundary gradient estimates for viscosity solutions to nonlinear free boundary problems with unbounded measurable ingredients	10
Increase of mass and nonlocal effects in the homogenization of magneto-elastodynamics problems	10
Derivation of the 1-D Groma–Balogh equations from the Peierls–Nabarro model	9
$$\mathcal {A}$$-caloric approximation and partial regularity for parabolic systems with Orlicz growth	9
Ground states of attractive Bose gases near the critical rotating velocity	9
Interior Hölder estimate for the linearized complex Monge–Ampère equation	9
On the equilibrium shape of a crystal	9
Homogenization of the Allen–Cahn equation with periodic mobility	9
A Bochner formula on path space for the Ricci flow	9
Stability estimates for the complex Monge-Ampère and Hessian equations	9
Fully non-linear elliptic equations on compact almost Hermitian manifolds	9
Trudinger–Moser and Hardy–Trudinger–Moser inequalities for the Aharonov–Bohm magnetic field	9
On the optimality and decay of p-Hardy weights on graphs	9
Line-tension limits for line singularities and application to the mixed-growth case	9
The Petty projection inequality for sets of finite perimeter	8
Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant	8

Unbounded mass radial solutions for the Keller–Segel equation in the disk	8
Homoclinics for singular strong force Lagrangian systems in $${\mathbb {R}}^N$$	8
Sharp decay estimates and asymptotic stability for incompressible MHD equations without viscosity or magnetic diffusion	8
Some conformally invariant gap theorems for Bach-flat 4-manifolds	8
An exterior overdetermined problem for Finsler N-Laplacian in convex cones	8
Dimension reduction through gamma convergence for general prestrained thin elastic sheets	8
Nonlinear scalar field $$(p_{1}, p_{2})$$-Laplacian equations in $$\mathbb {R}^{N}$$: existence and multiplicity	8
Fluctuation estimates for the multi-cell formula in stochastic homogenization of partitions	8
Interior Hessian estimates for a class of Hessian type equations	8
Local well-posedness of the 1d compressible Navier–Stokes system with rough data	7
Quantitative symmetry in a mixed Serrin-type problem for a constrained torsional rigidity	7
On the existence of closed $$C^{1,1}$$ curves of constant curvature	7
Regularity theory for non-autonomous problems with a priori assumptions	7
$$\displaystyle L^{\infty }$$-truncation of closed differential forms	7
Global Existence, Regularity and Boundedness in a Higher-dimensional Chemotaxis-Navier-Stokes System with Nonlinear Diffusion and General Sensitivity	7
Stable determination of an elastic medium scatterer by a single far-field measurement and beyond	7
Phase separation on varying surfaces and convergence of diffuse interface approximations	7
The obstacle problem for a higher order fractional Laplacian	7
The well-posedness of incompressible rotational jet flows with gravity	7
Ground states of spin-1 BEC with attractive mean-field interaction trapped in harmonic potential in $${\mathbb {R}}^2$$	7
Generalized Donaldson functionals and related nonlinear partial differential equations	7
Hölder regularity for parabolic fractional p-Laplacian	7
Stabilizing effect of magnetic field on the 2D ideal magnetohydrodynamic flow with mixed partial damping	7
Isoperimetric inequalities and regularity of A-harmonic functions on surfaces	7
Wolff potentials and measure data vectorial problems with Orlicz growth	7
Nonexistence of solutions to quasilinear parabolic equations with a potential in bounded domains	7
An obstacle problem arising from American options pricing: regularity of solutions	7
Quasilinear Schrödinger equations with concave and convex nonlinearities	7
Principal spectral curves for Lane–Emden fully nonlinear type systems and applications	7
Regularity of gradient vector fields giving rise to finite Caccioppoli partitions	7
Global wellposedness and asymptotic behavior of axisymmetric strong solutions to the vacuum free boundary problem of isentropic compressible Navier–Stokes equations	7
Conformal tori with almost non-negative scalar curvature	7
Optimal measure transportation with respect to non-traditional costs	7
Variable-coefficient parabolic theory as a high-dimensional limit of elliptic theory	7
Multiple constant sign and nodal solutions for nonlinear nonhomogeneous elliptic equations depending on a parameter	7
On a multi-objective control problem for the Korteweg–de Vries equation	7
A Liouville type result for fractional GJMS equations on higher dimensional spheres	6
Discrete infinity Laplace equations on graphs and tug-of-war games	6
Schrödinger-poisson system with zero mass in $$\mathbb {R}^2$$ involving (2, q)-Laplacian: existence, asymptotic behavior and regularity of solutions	6
Optimal decay for the 3D anisotropic Boussinesq equations near the hydrostatic balance	6
Korevaar–Schoen’s energy on strongly rectifiable spaces	6
Non-minimality of spirals in sub-Riemannian manifolds	6
Positive energy static solutions for the Chern–Simons–Schrödinger system under a large-distance fall-off requirement on the gauge potentials	6
Monge–Ampère operators and valuations	6
Global gradient estimates for the mixed local and nonlocal problems with measurable nonlinearities	6
Globally stable blowup profile for supercritical wave maps in all dimensions	6
Optimization of total population in logistic model with nonlocal dispersals and heterogeneous environments	6
Nonlinear stability of sinusoidal Euler flows on a flat two-torus	6
Orientability and asymptotic convergence of Q-tensor flow of biaxial nematic liquid crystals	6
The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge–Ampère measures	6
A variational setting for an indefinite Lagrangian with an affine Noether charge	6
Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility	6
Asymptotic behavior of the eigenfrequencies of a thin elastic rod with non-uniform cross-section of extremely oblate shape	6
On a novel gradient flow structure for the aggregation equation	6
Uniqueness of conformal-harmonic maps on locally conformally flat 4-manifolds	6
Onset of pattern formation in thin ferromagnetic films with perpendicular anisotropy	6
Long time behavior for a periodic Lotka–Volterra reaction–diffusion system with strong competition	6
On the prescribed scalar curvature problem with very degenerate prescribed functions	6
On $$W^{2,p}$$-estimates for solutions of obstacle problems for fully nonlinear elliptic equations with oblique boundary conditions	6
Uniqueness for linear integro-differential equations in the real line and applications	6
Geometry of generalized fluid flows	6
Convergence of semi-convex functions in CAT(1)-spaces	5
Weighted fractional Poincaré inequalities via isoperimetric inequalities	5
Asymptotic behavior of $$L^2$$-subcritical relativistic Fermi systems in the nonrelativistic limit	5
New weighted sharp Trudinger–Moser inequalities defined on the whole euclidean space $$ {\mathbb {R}}^N $$ and applications	5
Lower semicontinuity and relaxation for free discontinuity functionals with non-standard growth	5
Instability of Type (II) Lawson–Osserman cones	5
$$L^p$$-Hardy identities and inequalities with respect to the distance and mean distance to the boundary	5
Two generalized Tricomi equations	5
Existence and dynamics of normalized solutions to nonlinear Schrödinger equations with mixed fractional Laplacians	5
Gradient estimates for divergence form parabolic systems from composite materials	5
A unified approach to self-improving property via K-functionals	5
Correction to: “New weighted sharp Trudinger–Moser inequalities defined on the whole euclidean space $${\mathbb {R}}^N $$ and applications”	5
The effects of long-range interaction to wave propagation	5
Blow up analysis for a parabolic MEMS problem, I: Hölder estimate	5
Liouville type theorems for a quasilinear elliptic differential inequality with weighted nonlocal source and gradient absorption terms	5
Multiple high energy solutions for fractional Schrödinger equation with critical growth	5
Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations	5
A nonlocal free boundary problem with Wasserstein distance	5
Geometric analysis of the Yang–Mills connections over compact Kähler surfaces	5

Stability of quasi-entropy solutions of non-local scalar conservation laws	5
Global existence of classical solutions for a reactive polymeric fluid near equilibrium	5
Critical functions and blow-up asymptotics for the fractional Brezis–Nirenberg problem in low dimension	5
Absence of positive eigenvalues of magnetic Schrödinger operators	5
Concentration behavior of endemic equilibrium for a reaction–diffusion–advection SIS epidemic model with mass action infection mechanism	5
Steady-state Navier–Stokes flow in an obstructed pipe under mixed boundary conditions and with a prescribed transversal flux rate	5
Low Mach number limit for the global large solutions to the 2D Navier–Stokes–Korteweg system in the critical $$\widehat{L^p}$$ framework	5
The Neumann Green function and scale-invariant regularity estimates for elliptic equations with Neumann data in Lipschitz domains	5
Brezis–Van Schaftingen–Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo–Nirenberg inequalities	5
Geometry of complete minimal surfaces at infinity and the Willmore index of their inversions	5
Monotonicity-based inversion of fractional semilinear elliptic equations with power type nonlinearities	5
Hessian estimates for the Lagrangian mean curvature flow	5
Sharp quantitative stability of Poincaré-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows	5
The rigidity of minimal Legendrian submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices	5
Nonlocal Harnack inequalities in the Heisenberg group	5
Eventual smoothness and stabilization in a three-dimensional Keller–Segel–Navier–Stokes system with rotational flux	5
De Giorgi’s inequality for the thresholding scheme with arbitrary mobilities and surface tensions	5
Weak KAM theory for action minimizing random walks	5
Qualitative properties of nonnegative solutions of some semilinear elliptic equations in cylindrical domains	5
Characterization of symmetric polyconvexity in higher dimensions	5
Liouville type theorems for positive harmonic functions on the unit ball with a nonlinear boundary condition	4
Uniqueness when the $$L_p$$ curvature is close to be a constant for $$p\in [0,1)$$	4
On p-harmonic self-maps of spheres	4
A sharp convergence theorem for the mean curvature flow in the sphere	4
The generalized porous medium equation on graphs: existence and uniqueness of solutions with $$\ell ^1$$ data	4
$$\Gamma $$-convergence and stochastic homogenisation of singularly-perturbed elliptic functionals	4
Extensions and traces of BV functions in rough domains and generalized Cheeger sets	4
Harnack inequality for nonlocal operators on manifolds with nonnegative curvature	4
On the Morse index of critical points in the viscosity method	4
Curvature estimates for semi-convex solutions of Hessian equations in hyperbolic space	4
Volume minimising unit vector fields on three dimensional space forms of positive curvature	4
Dispersive estimates for 1D matrix Schrödinger operators with threshold resonance	4
A vectorial problem with thin free boundary	4
Convergence to the grim reaper for a curvature flow with unbounded boundary slopes	4
Regularity for quasi-linear parabolic equations with nonhomogeneous degeneracy or singularity	4
On the compactness of Hamiltonian stationary Lagrangian surfaces in Kähler surfaces	4
Perturbation limiting behaviors of normalized ground states to focusing mass-critical Hartree equations with Local repulsion	4
Upper heat kernel estimates for nonlocal operators via Aronson’s method	4
A Poincaré type inequality with three constraints	4
Boundary expansions of complete conformal metrics with negative Ricci curvatures	4
Bubbling phenomenon for semilinear Neumann elliptic equations of critical exponential growth	4
Well-posedness of the two-dimensional Abels–Garcke–Grün model for two-phase flows with unmatched densities	4
Elliptic methods for solving the linearized field equations of causal variational principles	4
Classification of the spreading behaviors of a two-species diffusion-competition system with free boundaries	4
Optimal regularity of isoperimetric sets with Hölder densities	4
Normalized solutions for Schrödinger equations with mixed dispersion and critical exponential growth in $${\mathbb {R}}^2$$	4
Overdetermined problems for fully nonlinear equations with constant Dirichlet boundary conditions in space forms	4
Operator-norm homogenisation estimates for the system of Maxwell equations on periodic singular structures	4
Trace inequalities of the Sobolev type and nonlinear Dirichlet problems	4
Apriori decay estimates for Hardy–Sobolev–Maz’ya equations	4
On the planar Schrödinger equation with indefinite linear part and critical growth nonlinearity	4
Rigidity and deformation of generalized sphere packings on 3-dimensional manifolds with boundary	4
Regularity properties for quasiminimizers of a (p, q)-Dirichlet integral	4
Weak stabilization in degenerate parabolic equations in divergence form: application to degenerate Keller–Segel systems	4
Gradient potential estimates in elliptic obstacle problems with Orlicz growth	4
Anisotropic surface tensions for phase transitions in periodic media	4
On the global well-posedness and scattering of the 3D Klein–Gordon–Zakharov system	4
Riemannian metrics with prescribed volume and finite parts of Dirichlet spectrum	4
Two short closed geodesics on a sphere of odd dimension	4
Local well-posedness for incompressible neo-Hookean elastic equations in almost critical Sobolev spaces	4
Classification of finite Morse index solutions to the polyharmonic Hénon equation	4
Resolvent estimates for wave operators in Lipschitz domains	4
Stability of the viscoelastic Rayleigh–Bénard problem with an upper free boundary	4
Uniqueness of global weak solutions for the general Ericksen–Leslie system with Ginzburg–Landau penalization in $${\mathbb {T}}^2$$	4
Partial existence result for homogeneous quasilinear parabolic problems beyond the duality pairing	4
Multiple solutions for (p, q)-Laplacian equations in $$\mathbb {R}^N$$ with critical or subcritical exponents	4
Clustering of boundary interfaces for an inhomogeneous Allen–Cahn equation on a smooth bounded domain	4
A compactness result for scalar-flat metrics on low dimensional manifolds with umbilic boundary	4
Limits of density-constrained optimal transport	4
Critical Hardy inequality on the half-space via the harmonic transplantation	4
Curvature estimates for stable minimal surfaces with a common free boundary	4
On nonminimizing solutions of elliptic free boundary problems	3
Existence and decays of solutions for fractional Schrödinger equations with general potentials	3
Regularity in the two-phase Bernoulli problem for the p-Laplace operator	3
Multi-bump solutions to Schrödinger-Poisson equations with critical growth in $${\mathbb {R}}^3$$	3
Regularity of the $$p-$$Bergman kernel	3
Deformation of framed curves with boundary conditions	3
On time-splitting methods for gradient flows with two dissipation mechanisms	3
Interior $$W^{2,p}$$ estimate for small perturbations to the complex Monge–AmpÈre equation	3
Relationship between variational problems with norm constraints and ground state of semilinear elliptic equations in $$\mathbb {R}^2$$	3
The evolution Navier–Stokes equations in a cube under Navier boundary conditions: rarefaction and uniqueness of global solutions	3
An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces	3
Pure Neumann problem for slightly supercritical Lane-Emden system	3
An alternative proof for small energy implies regularity for radially symmetric $$(1+2)$$-dimensional wave maps	3
On the Minkowski problem for p-harmonic measures	3
Choquard equations with saturable reaction	3
Free boundary CMC annuli in spherical and hyperbolic balls	3
Long time behaviour of the discrete volume preserving mean curvature flow in the flat torus	3
Existence, sign and asymptotic behaviour for a class of integro-differential elliptic type problems	3
Transition fronts of combustion reaction–diffusion equations around an obstacle	3
A priori estimates and Liouville-type theorems for the semilinear parabolic equations involving the nonlinear gradient source	3
Existence and uniqueness of bounded stable solutions to the Peierls–Nabarro model for curved dislocations	3
Harnack inequalities and quantization properties for the $$n-$$Liouville equation	3
Existence of nontopological solutions of the self-dual Einstein-Maxwell-Higgs equations on compact surfaces	3
Stochastic homogenization of quasiconvex degenerate viscous HJ equations in 1d	3