Calculus of Variations and Partial Differential Equations

Article	Citations
Quadratically pinched hypersurfaces of the sphere via mean curvature flow with surgery	81
The well-posedness of incompressible rotational jet flows with gravity	38
On the equilibrium shape of a crystal	37
On the optimality and decay of p-Hardy weights on graphs	36
Geometry of complete minimal surfaces at infinity and the Willmore index of their inversions	36
Sharp decay estimates and asymptotic stability for incompressible MHD equations without viscosity or magnetic diffusion	35
Characterization of symmetric polyconvexity in higher dimensions	32
Conformal tori with almost non-negative scalar curvature	30
The rigidity of minimal Legendrian submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices	28
Upper bounds for the Steklov eigenvalues on trees	27
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	25
On a multi-objective control problem for the Korteweg–de Vries equation	24
Principal spectral curves for Lane–Emden fully nonlinear type systems and applications	23
Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem	23
Regularity theory for non-autonomous problems with a priori assumptions	22
Dichotomous concentrating solutions for a Schrödinger–Newton equation	22
Serrin–type regularity criteria for the 3D MHD equations via one velocity component and one magnetic component	21
Vanishing-concentration-compactness alternative for critical Sobolev embedding with a general integrand in $$\mathbb R^2$$	20
Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant	20
Second order $$L_p$$ estimates for subsolutions of fully nonlinear equations	19
Sharp quantitative stability of Poincaré-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows	19
Hölder regularity for parabolic fractional p-Laplacian	18
Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities	17
Stable determination of an elastic medium scatterer by a single far-field measurement and beyond	17
Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations	17

Wolff potentials and measure data vectorial problems with Orlicz growth	17
Concentration behavior of endemic equilibrium for a reaction–diffusion–advection SIS epidemic model with mass action infection mechanism	16
Multi-peak solutions for semilinear elliptic equations with nearly critical Sobolev exponents in lower dimensions	16
Improved regularity for the parabolic normalized p-Laplace equation	16
Trudinger–Moser and Hardy–Trudinger–Moser inequalities for the Aharonov–Bohm magnetic field	16
Nonlinear stability of sinusoidal Euler flows on a flat two-torus	16
Scattering for the non-radial inhomogenous biharmonic NLS equation	15
On a novel gradient flow structure for the aggregation equation	15
One-dimensional symmetry of positive bounded solutions to the subcubic and cubic nonlinear Schrödinger equation in the half-space in dimensions $$N=4,5$$	15
A vectorial problem with thin free boundary	14
Free boundary CMC annuli in spherical and hyperbolic balls	14
Caffarelli–Kohn–Nirenberg inequalities for curl-free vector fields and second order derivatives	14
A priori estimates and Liouville-type theorems for the semilinear parabolic equations involving the nonlinear gradient source	14
An Intrinsic Harnack inequality for some non-homogeneous parabolic equations in non-divergence form	14
Compactness for a class of integral functionals with interacting local and non-local terms	14
On p-harmonic self-maps of spheres	14
Scalar and mean curvature comparison via $$\mu $$-bubbles	13
Local boundedness for solutions of a class of nonlinear elliptic systems	13
Local solvability of the Poisson equation for closed $$G_2$$-structures	13
Existence and nonexistence in the liquid drop model	13
Correction: a comparison principle for semilinear Hamilton–Jacobi–Bellman equations in the Wasserstein space	13
Normalized solutions for Schrödinger equations with mixed dispersion and critical exponential growth in $${\mathbb {R}}^2$$	13
Small order asymptotics for nonlinear fractional problems	12
Discrete Carleman estimates and three balls inequalities	12
Long time behaviour of the discrete volume preserving mean curvature flow in the flat torus	12
The Euler–Helfrich functional	12
Weak stabilization in degenerate parabolic equations in divergence form: application to degenerate Keller–Segel systems	12
Apriori decay estimates for Hardy–Sobolev–Maz’ya equations	12
Riemannian metrics with prescribed volume and finite parts of Dirichlet spectrum	11
Blow up analysis for a parabolic MEMS problem, I: Hölder estimate	11
Sharp anisotropic singular Trudinger–Moser inequalities in the entire space	11
Sharp estimates and non-degeneracy of low energy nodal solutions for the Lane–Emden equation in dimension two	11
Local well-posedness for incompressible neo-Hookean elastic equations in almost critical Sobolev spaces	11
Convergence of semi-convex functions in CAT(1)-spaces	11
Front propagation and blocking of time periodic bistable reaction-diffusion equations in cylindrical domains	11
Hypersurfaces of $$\mathbb {S}^2\times \mathbb {S}^2$$ with constant sectional curvature	10
On blow up for a class of radial Hartree type equations	10
Minimisers of supremal functionals and mass-minimising 1-currents	10
On the singular planar Plateau problem	10
Steady-state Navier–Stokes flow in an obstructed pipe under mixed boundary conditions and with a prescribed transversal flux rate	10
Brezis–Van Schaftingen–Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo–Nirenberg inequalities	10
Phase transition of an anisotropic Ginzburg–Landau equation	10
Weighted fractional Poincaré inequalities via isoperimetric inequalities	10
Overdetermined problems for fully nonlinear equations with constant Dirichlet boundary conditions in space forms	10
Normalized multi-bump solutions of nonlinear Schrödinger equations via variational approach	9
Uniqueness of weak solutions of the Plateau flow	9
On the entire self-shrinking solutions to Lagrangian mean curvature flow II	9
Saturn ring defect around a spherical particle immersed in a nematic liquid crystal	9
Semiclassical states for nonlinear Dirac equations with singular potentials	9
On the hydrostatic Navier–Stokes equations with Gevrey class 2 data	9

From radial symmetry to fractal behavior of aggregation equilibria for repulsive–attractive potentials	9
Hardy–Sobolev interpolation inequalities	9
Local pointwise second derivative estimates for strong solutions to the $$\sigma _k$$-Yamabe equation on Euclidean domains	9
Regularity estimates for fully nonlinear elliptic PDEs with general Hamiltonian terms and unbounded ingredients	9
A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers	9
The dual $$p$$-convex functions and its applications	9
Fujita-type theorems for a nonlocal quasilinear parabolic differential inequality	9
Conformal Dirac–Einstein equations on manifolds with boundary.	9
Isoperimetric inequalities and geometry of level curves of harmonic functions on smooth and singular surfaces	9
Boundary regularity of an isotropically censored nonlocal operator	9
Optimal coordinates for Ricci-flat conifolds	8
On the second Robin eigenvalue of the Laplacian	8
Infinitely many periodic solutions for the quasi-linear Euler–Bernoulli beam equation with fixed ends	8
Quantitative stability of harmonic maps from $${\mathbb {R}}^2$$ to $${\mathbb {S}}^2$$ with a higher degree	8
Conservation laws for even order elliptic systems in the critical dimension - a new approach	8
Graphical mean curvature flow with bounded bi-Ricci curvature	8
On the two dimensional fast phase transition equation: well-posedness and long-time dynamics	8
On potentials whose level sets are orbits	8
On evolutionary problems with a-priori bounded gradients	8
A chemotaxis system with singular sensitivity for burglaries in the higher-dimensional settings: generalized solvability and long-time behavior	8
Partially regular weak solutions of the stationary Navier-Stokes equations in dimension 6	8
On convex functions and elliptic operators	8
Blow up solutions for Sinh-Gordon equation with residual mass	8
Roles of density-related diffusion and signal-dependent motilities in a chemotaxis–consumption system	8
Approaching the isoperimetric problem in $$H_{{\mathbb {C}}}^m$$ via the hyperbolic log-convex density conjecture	8
The compressible Euler system with nonlocal pressure: global existence and relaxation	8
On rectifiable measures in Carnot groups: representation	8
Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group	8
Explicit forms for extremals of sharp Sobolev trace inequalities on the unit balls	7
Periodic solution for Hamiltonian type systems with critical growth	7
Harnack’s estimate for a mixed local–nonlocal doubly nonlinear parabolic equation	7
$$L^\infty $$ continuation principle to the compressible non-isothermal nematic liquid crystal flows with zero heat conduction and vacuum	7
Energy scattering for radial focusing inhomogeneous bi-harmonic Schrödinger equations	7
Riesz transforms of a general Ornstein–Uhlenbeck semigroup	7
Prescribing the gauss curvature of convex bodies in hyperbolic space	7
Higher regularity for weak solutions to degenerate parabolic problems	7
A free boundary isometric embedding problem in the unit ball	7
On nonlinear instability of liquid Lane–Emden stars	7
The symmetric (log-)epiperimetric inequality and a decay-growth estimate	7
Continuity of s-minimal functions	7
The anisotropic Gaussian isoperimetric inequality and Ehrhard symmetrization	7
Absolutely continuous and BV-curves in 1-Wasserstein spaces	7
Augmented Lagrangian methods for degenerate Hamilton–Jacobi equations	7
On the random G equation with nonzero divergence	7
The equality cases in Steiner’s projection inequality	7
Multiple solutions and profile description for a nonlinear Schrödinger–Bopp–Podolsky–Proca system on a manifold	7
Manifolds for which Huber’s Theorem holds	7
Surface measure on, and the local geometry of, sub-Riemannian manifolds	7
Rigidity and $$\varepsilon $$-regularity theorems of Ricci shrinkers	7
A universal variational framework for parabolic equations and systems	7
Existence of minimizers for causal variational principles on compact subsets of momentum space in the homogeneous setting	7
Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast	7
Hardy and Rellich inequality on lattices	7
Convergence rates for the Allen–Cahn equation with boundary contact energy: the non-perturbative regime	7
Rigidity of Finsler gradient steady Ricci soliton	6
Smooth approximation of mappings with rank of the derivative at most 1	6
Isolated singularities for the n-Liouville equation	6
Mixed boundary valued problems for linear and nonlinear wave equations in domains with fractal boundaries	6
A strong form of the quantitative Wulff inequality for crystalline norms	6
Global spherically symmetric solutions to degenerate compressible Navier-Stokes equations with large data and far field vacuum	6
Regularity for nonlocal problems with non-standard growth	6
Regularized mean curvature flow for invariant hypersurfaces in a Hilbert space and its application to gauge theory	6
Superharmonicity of curvature function for the convex level sets of harmonic functions	6
Extension operators and Korn inequality for variable coefficients in perforated domains with applications to homogenization of viscoelastic non-simple materials	6
A Maupertuis-type principle in relativistic mechanics and applications	6
The Demailly system for a direct sum of ample line bundles on Riemann surfaces	6
Traveling vortex pairs for 2D incompressible Euler equations	6
On the free boundary problems for the ideal incompressible MHD equations	6
Stability of spectral partitions and the Dirichlet-to-Neumann map	6
Symmetric matrices, signed graphs, and nodal domain theorems	6
A class of fourth-order dispersive wave equations with exponential source	6
Quasistatic evolution in magnetoelasticity under subcritical coercivity assumptions	6
Multiplicity of positive solutions for mixed local-nonlocal singular critical problems	6
Prescribing discrete Gaussian curvature on polyhedral surfaces	6
Bernstein type theorems of translating solitons of the mean curvature flow in higher codimension	6
Generalized neck analysis of harmonic maps from surfaces	6
A variational characterization of calibrated submanifolds	6
The avoidance principle for noncompact hypersurfaces moving by mean curvature flow	6
The spreading of global solutions of chemotaxis systems with logistic source and consumption on $$\mathbb {R}^{N}$$	6
Homogenisation of dynamical optimal transport on periodic graphs	6

$$C^{1,\alpha }$$ regularity of hypersurfaces of bounded nonlocal mean curvature in Riemannian manifolds	6
Stable surfaces and free boundary marginally outer trapped surfaces	6
Variational aspects of phase transitions with prescribed mean curvature	6
Bourgain-Brezis-Mironescu formula for $$W^{s,p}_q$$-spaces in arbitrary domains	6
On the Morse index of branched Willmore spheres in 3-space	6
Low Mach number limit for the global large solutions to the 2D Navier–Stokes–Korteweg system in the critical $$\widehat{L^p}$$ framework	5
Some elliptic problems involving the gradient on general bounded and exterior domains	5
Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot groups of step two	5
Long time behavior for a periodic Lotka–Volterra reaction–diffusion system with strong competition	5
Perturbed Schrödinger lattice systems with superlinear terms: Multiplicity of homoclinic solutions	5
Absence and presence of Lavrentiev’s phenomenon for double phase functionals upon every choice of exponents	5
Energy identity and necklessness for $$\alpha $$-Dirac-harmonic maps into a sphere	5
Derivation of the 1-D Groma–Balogh equations from the Peierls–Nabarro model	5
Orientability and asymptotic convergence of Q-tensor flow of biaxial nematic liquid crystals	5
Volume minimising unit vector fields on three dimensional space forms of positive curvature	5
Partial existence result for homogeneous quasilinear parabolic problems beyond the duality pairing	5
Rigidity of min–max minimal disks in 3-balls with non-negative Ricci curvature	5
Global gradient estimates for the mixed local and nonlocal problems with measurable nonlinearities	5
Gauss curvature flow with an obstacle	5
Stability of quasi-entropy solutions of non-local scalar conservation laws	5
Hessian estimates for the Lagrangian mean curvature flow	5
On the equivalence between an Onofri-type inequality by Del Pino–Dolbeault and the sharp logarithmic Moser–Trudinger inequality	5
Sharp conditions for the linearization of finite elasticity	5
Regularity for quasi-minima of the Alt–Caffarelli functional	5
Notes on generalized special Lagrangian equation	5
Harnack-type estimates and extinction in finite time for a class of anisotropic porous medium type equations	5
Harnack inequality for nonlocal operators on manifolds with nonnegative curvature	5
Dirichlet problem for degenerate Hessian quotient type curvature equations	5
Nonlinear Schrödinger systems with trapping potentials for mixed attractive and repulsive interactions	5
Quantitative estimates in elliptic homogenization of non-divergence form with unbounded drifts and an interface	5
Unbounded mass radial solutions for the Keller–Segel equation in the disk	5
A planar Schrödinger–Newton system with Trudinger–Moser critical growth	5
Blow-up solutions for a system of Schrödinger equations with general quadratic-type nonlinearities in dimensions five and six	5
Local behavior of positive solutions of higher order conformally invariant equations with a singular set	5
Non-minimality of spirals in sub-Riemannian manifolds	5
Global well-posedness of 3D homogeneous and inhomogeneous MHD system with small unidirectional derivative	5
On the global well-posedness and scattering of the 3D Klein–Gordon–Zakharov system	5
Correction to: Two generalized Tricomi equations	5
Existence and orbital stability/instability of standing waves with prescribed mass for the $$L^{2}$$-supercritical NLS in bounded domains and exterior domains	5
Renormalized energy between fractional vortices with topologically induced free discontinuities on 2-dimensional Riemannian manifolds	5
Regularity for quasi-linear parabolic equations with nonhomogeneous degeneracy or singularity	4
Stochastic homogenization and effective Hamiltonians of Hamilton–Jacobi equations in one space dimension: the double-well case	4
On the Dirichlet problem for a class of fully nonlinear elliptic equations	4
Existence of ground state solutions to some Nonlinear Schrödinger equations on lattice graphs	4
Optimal $$C^\infty $$-approximation of functions with exponentially or sub-exponentially integrable derivative	4
Regularity theory and Green’s function for elliptic equations with lower order terms in unbounded domains	4
Gradient estimates for multi-phase problems	4
The Einstein-scalar field Lichnerowicz equations on graphs	4
Radial symmetry of solutions to anisotropic and weighted diffusion equations with discontinuous nonlinearities	4
Dirichlet problem for Krylov type equation in conformal geometry	4
Bubbling phenomenon for semilinear Neumann elliptic equations of critical exponential growth	4
Second order necessary condition for a strong minimum in the classical problem of calculus of variations	4
Spectral invariants of the perturbed polyharmonic Steklov problem	4
Boundary plasmas for a confined plasma problem in dimensional two	4
Deformation of discrete conformal structures on surfaces	4
Scattering for three waves nonlinear Schrödinger system with mass-resonance in 5D	4
Non-uniqueness in law for the Boussinesq system forced by random noise	4
Frankel’s property for free boundary minimal hypersurfaces in the Riemannian Schwarzschild manifolds	4
Multisolitons are the unique constrained minimizers of the KdV conserved quantities	4
Groundstates and infinitely many high energy solutions to a class of nonlinear Schrödinger–Poisson systems	4
Existence of periodic orbits and horseshoes for semiflows on a separable Banach space	4
Existence of singular isoperimetric regions in 8-dimensional manifolds	4
Upper heat kernel estimates for nonlocal operators via Aronson’s method	4
Fractional integration and optimal estimates for elliptic systems	4
Transition fronts of combustion reaction–diffusion equations around an obstacle	4
Density of Lipschitz functions in energy	4
Foliation of area minimizing hypersurfaces in asymptotically flat manifolds and Schoen’s conjecture	4
Curvature estimates for semi-convex solutions of Hessian equations in hyperbolic space	4
The Dirichlet-to-Neumann operator associated with the 1-Laplacian and evolution problems	4
Prescribed mass standing waves for energy critical Hartree equations	4
Uniqueness and positivity issues in a quasilinear indefinite problem	4
On Lipschitz Geometry at infinity of complex analytic sets	4
Linear inverse problems with Hessian–Schatten total variation	4
Infinitely many nodal solutions of Kirchhoff-type equations with asymptotically cubic nonlinearity without oddness hypothesis	4
A Talenti-type comparison theorem for $${{\,\mathrm{RCD}\,}}(K,N)$$ spaces and applications	4
EDP-convergence for a linear reaction-diffusion system with fast reversible reaction	4
Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings	4
Characterisation of gradient flows for a given functional	4
Axisymmetric steady Navier–Stokes flows under suction	4
Sharp uncertainty principles on metric measure spaces	4
Volume comparison theorem with respect to sigma-k curvature	4
Singular solutions to the $$\sigma _k$$-Yamabe equation with prescribed asymptotics	4
The effects of dispersal and spatial heterogeneity on the dynamics of a predator–prey model	4
Mass, center of mass and isoperimetry in asymptotically flat 3-manifolds	4
Approximation of partial differential equations on compact resistance spaces	4
Asymptotic behavior of $$L^2$$-subcritical relativistic Fermi systems in the nonrelativistic limit	4
A Rademacher type theorem for Hamiltonians H(x, p) and an application to absolute minimizers	3
Global dynamics of large solution for the compressible Navier–Stokes–Korteweg equations	3
Excited states of Bose–Einstein condensates with degenerate attractive interactions	3
Density and positive mass theorems for incomplete manifolds	3
Effect of the average scalar curvature on Riemannian manifolds	3
Determinant majorization and the work of Guo-Phong-Tong and Abja-OLive	3
Layer dynamics for the one dimensional $$\varvec{\varepsilon }$$-dependent Cahn–Hilliard/Allen–Cahn equation	3
Convergence rate of general entropic optimal transport costs	3
Schrödinger equation in dimension two with competing logarithmic self-interaction	3