Calculus of Variations and Partial Differential Equations

Article	Citations
Characterization of symmetric polyconvexity in higher dimensions	54
The rigidity of minimal Legendrian submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices	50
On the optimality and decay of p-Hardy weights on graphs	46
Improved regularity for the parabolic normalized p-Laplace equation	42
Concavity for elliptic and parabolic equations in locally symmetric spaces with nonnegative curvature	36
Second order $$L_p$$ estimates for subsolutions of fully nonlinear equations	34
On a novel gradient flow structure for the aggregation equation	31
Kähler Soliton Surfaces Are Generically Toric	30
Sharp $$\textrm{L}^\infty $$ estimates for fully non-linear elliptic equations on compact complex manifolds	29
On Rabinowitz’s minimal period conjecture and subharmonic solutions for the wave equation on a disk	29
On a multi-objective control problem for the Korteweg–de Vries equation	29
Sharp quantitative stability of Poincaré-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows	26
Optimal Hölder convergence of a class of singular steady states to the Bahouri–Chemin patch	24
Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem	23
Wolff potentials and measure data vectorial problems with Orlicz growth	23
The well-posedness of incompressible rotational jet flows with gravity	20
Comparison theorems on H-type sub-Riemannian manifolds	20
On polynomial solutions to the minimal surface equation	20
Principal spectral curves for Lane–Emden fully nonlinear type systems and applications	18
Regularity theory for non-autonomous problems with a priori assumptions	18
On the equilibrium shape of a crystal	18
Dichotomous concentrating solutions for a Schrödinger–Newton equation	17
Multi-peak solutions for semilinear elliptic equations with nearly critical Sobolev exponents in lower dimensions	17
Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations	17
Trudinger–Moser and Hardy–Trudinger–Moser inequalities for the Aharonov–Bohm magnetic field	17

Nonlinear stability of sinusoidal Euler flows on a flat two-torus	17
First critical field in the pinned three-dimensional Ginzburg–Landau model of superconductivity	17
Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant	17
Hölder regularity for parabolic fractional p-Laplacian	17
Geometry of complete minimal surfaces at infinity and the Willmore index of their inversions	16
Sharp decay estimates and asymptotic stability for incompressible MHD equations without viscosity or magnetic diffusion	16
Caffarelli–Kohn–Nirenberg inequalities for curl-free vector fields and second order derivatives	15
On the stability of the annulus for the torsion of multiply connected domains	15
The asymptotic behavior of discrete Schrödinger equation on the hexagonal triangulation	15
Free boundary CMC annuli in spherical and hyperbolic balls	15
Local solvability of the Poisson equation for closed $$G_2$$-structures	15
The Riemannian hemisphere is almost calibrated in the injective hull of its boundary	14
On the Yamabe invariant of certain compact manifolds with boundary	14
A priori estimates and Liouville-type theorems for the semilinear parabolic equations involving the nonlinear gradient source	14
Hamilton-Ivey estimates for gradient Ricci solitons	14
On the singular planar Plateau problem	14
Variational analysis of nonlocal Dirichlet problems in periodically perforated domains	14
Riemannian metrics with prescribed volume and finite parts of Dirichlet spectrum	14
On blow up for a class of radial Hartree type equations	13
A vectorial problem with thin free boundary	13
Convergence of semi-convex functions in CAT(1)-spaces	13
Weighted fractional Poincaré inequalities via isoperimetric inequalities	13
Sharp estimates and non-degeneracy of low energy nodal solutions for the Lane–Emden equation in dimension two	13
Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs	12
Front propagation and blocking of time periodic bistable reaction-diffusion equations in cylindrical domains	12
Variational structures for the Fokker–Planck equation with general Dirichlet boundary conditions	12
On functionals involving the p-capacity and the q-torsional rigidity	12
Brezis–Van Schaftingen–Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo–Nirenberg inequalities	12
Steady-state Navier–Stokes flow in an obstructed pipe under mixed boundary conditions and with a prescribed transversal flux rate	12
Local well-posedness for incompressible neo-Hookean elastic equations in almost critical Sobolev spaces	11
Correction: a comparison principle for semilinear Hamilton–Jacobi–Bellman equations in the Wasserstein space	11
Overdetermined problems for fully nonlinear equations with constant Dirichlet boundary conditions in space forms	11
On p-harmonic self-maps of spheres	11
Compactness for a class of integral functionals with interacting local and non-local terms	11
Long time behaviour of the discrete volume preserving mean curvature flow in the flat torus	11
$$C^\alpha $$-well-posedness of first order degenerate differential equations in banach spaces	11
Conformal Dirac–Einstein equations on manifolds with boundary.	10
Singularity Formation for the Higher Dimensional Skyrme Model	10
Hypersurfaces of $$\mathbb {S}^2\times \mathbb {S}^2$$ with constant sectional curvature	10
Blow up analysis for a parabolic MEMS problem, I: Hölder estimate	10
Ground states for the NLS equation with combined nonlinearity on periodic metric graphs	10
A generalization of Savin’s small perturbation theorem for fully nonlinear elliptic equations and applications	10
Optimal coordinates for Ricci-flat conifolds	10
The $$L_{p}$$ dual Christoffel-Minkowski problem for $$1<p<q\le k+1$$ with $$1\le k\le n$$	10
Boundary regularity of an isotropically censored nonlocal operator	10
Nonlocal critical elliptic equations in homogeneous fractional Sobolev spaces	10
Normalized solutions for Schrödinger equations with mixed dispersion and critical exponential growth in $${\mathbb {R}}^2$$	10
Scalar and mean curvature comparison via $$\mu $$-bubbles	10
Minimisers of supremal functionals and mass-minimising 1-currents	10
On the hydrostatic Navier–Stokes equations with Gevrey class 2 data	10

On Blowup of Regularized Solutions to Jang Equation and Constant Null Expansion Surfaces	10
Graphical mean curvature flow with bounded bi-Ricci curvature	10
Global well-posedness for the Keller–Segel–Navier–Stokes system with nonlinear boundary conditions	10
Fujita-type theorems for a nonlocal quasilinear parabolic differential inequality	10
Rigidity and Łojasiewicz inequalities for Clifford self-shrinkers	10
Sharp anisotropic singular Trudinger–Moser inequalities in the entire space	10
Graphs with positive Lin-Lu-Yau curvature without quadrilaterals	10
Convergence of interfaces in boundary reactions	10
Uniqueness of weak solutions of the Plateau flow	10
On the entire self-shrinking solutions to Lagrangian mean curvature flow II	10
Blow up dynamics for the 3D energy-critical nonlinear Schrödinger equation	9
Symmetry of uniformly rotating solutions for the vortex-wave system	9
Best constants in subelliptic fractional Sobolev and Gagliardo-Nirenberg inequalities and ground states on stratified Lie groups	9
Asymptotic expansions for conformal scalar curvature equations near isolated singularities	9
Local minimizers in 3d of vector Allen-Cahn with a quadruple junction.	9
Some results on a gradient system with concave-convex and supercritical nonlinearities	9
Phase transition of an anisotropic Ginzburg–Landau equation	9
Regularity for free boundary surfaces minimizing degenerate area functionals	9
The dual $$p$$-convex functions and its applications	9
A Liouville property for eternal solutions to a supercritical semilinear heat equation	9
From radial symmetry to fractal behavior of aggregation equilibria for repulsive–attractive potentials	9
Hardy–Sobolev interpolation inequalities	9
A Cheeger inequality for the drift Laplacian with Wentzell boundary condition	8
A chemotaxis system with singular sensitivity for burglaries in the higher-dimensional settings: generalized solvability and long-time behavior	8
A multi-point maximum principle to prove global Harnack inequalities for Schrödinger operators	8
Stationary p–harmonic maps approaching planar singular harmonic maps to the circle	8
Global dynamics of the toxicant-taxis model with Robin boundary conditions	8
On potentials whose level sets are orbits	8
Rigidity and $$\varepsilon $$-regularity theorems of Ricci shrinkers	8
The anisotropic Gaussian isoperimetric inequality and Ehrhard symmetrization	8
Blow up solutions for Sinh-Gordon equation with residual mass	8
The compressible Euler system with nonlocal pressure: global existence and relaxation	8
Infinitely many periodic solutions for the quasi-linear Euler–Bernoulli beam equation with fixed ends	8
Harnack’s estimate for a mixed local–nonlocal doubly nonlinear parabolic equation	8
Dispersive estimates for Dirac Operators in dimension four with obstructions at threshold energies	8
Quantitative stability of harmonic maps from $${\mathbb {R}}^2$$ to $${\mathbb {S}}^2$$ with a higher degree	8
Roles of density-related diffusion and signal-dependent motilities in a chemotaxis–consumption system	8
Partial regularity of optimal transport with Coulomb cost	8
On a degenerate elliptic equation with Hardy potential	8
Gradient continuity estimates for elliptic equations of p-Laplace type with measure data	8
Topology of complete minimal submanifolds in $${\mathbb {R}}^{n+m}$$ with finite total curvature	8
A universal variational framework for parabolic equations and systems	8
On the second Robin eigenvalue of the Laplacian	8
On evolutionary problems with a-priori bounded gradients	8
Continuity of s-minimal functions	8
Approaching the isoperimetric problem in $$H_{{\mathbb {C}}}^m$$ via the hyperbolic log-convex density conjecture	8
The equality cases in Steiner’s projection inequality	7
Hardy and Rellich inequality on lattices	7
Manifolds for which Huber’s Theorem holds	7
Local Lipschitz continuity of the minimizers of nonuniformly convex functionals under the Lower Bounded Slope Condition	7
Bifurcations in Lagrangian systems and geodesics I	7
Higher regularity for weak solutions to degenerate parabolic problems	7
Convergence rates for the Allen–Cahn equation with boundary contact energy: the non-perturbative regime	7
The symmetric (log-)epiperimetric inequality and a decay-growth estimate	7
Prescribing the gauss curvature of convex bodies in hyperbolic space	7
Absolutely continuous and BV-curves in 1-Wasserstein spaces	7
Homogenisation of dynamical optimal transport on periodic graphs	7
Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast	7
Periodic solution for Hamiltonian type systems with critical growth	7
On the free boundary problems for the ideal incompressible MHD equations	7
On nonlinear instability of liquid Lane–Emden stars	7
Symmetry breaking for local minimizers of a free discontinuity problem	7
On the random G equation with nonzero divergence	7
Explicit forms for extremals of sharp Sobolev trace inequalities on the unit balls	7
Prescribing negative curvature with cusps and conical singularities on compact surface	7
Surface measure on, and the local geometry of, sub-Riemannian manifolds	7
The spreading of global solutions of chemotaxis systems with logistic source and consumption on $$\mathbb {R}^{N}$$	7
Asymptotic stability of composite waves of viscous shock and rarefaction for relaxed compressible Navier-Stokes equations	7
Stability of spectral partitions and the Dirichlet-to-Neumann map	7
Lusin approximation for functions of bounded variation	7
New applications of Hadamard-in-the-mean inequalities to incompressible variational problems	7
Quasistatic evolution in magnetoelasticity under subcritical coercivity assumptions	6
The existence and stability of solutions for liquid crystal two-phase interface problems	6
Smooth approximation of mappings with rank of the derivative at most 1	6
A strong form of the quantitative Wulff inequality for crystalline norms	6
The Demailly system for a direct sum of ample line bundles on Riemann surfaces	6
A class of fourth-order dispersive wave equations with exponential source	6
Global spherically symmetric solutions to degenerate compressible Navier-Stokes equations with large data and far field vacuum	6
Graphs with Lin-Lu-Yau curvature at least one and regular bone-idle graphs	6
Multiple solutions and profile description for a nonlinear Schrödinger–Bopp–Podolsky–Proca system on a manifold	6

The ultimate shape of solution to the $$\varvec{L_p}$$ Minkowski problem	6
On the equivalence between an Onofri-type inequality by Del Pino–Dolbeault and the sharp logarithmic Moser–Trudinger inequality	6
Regularized mean curvature flow for invariant hypersurfaces in a Hilbert space and its application to gauge theory	6
Rigidity of Finsler gradient steady Ricci soliton	6
Extension operators and Korn inequality for variable coefficients in perforated domains with applications to homogenization of viscoelastic non-simple materials	6
Global existence for the fully parabolic Keller–Segel system with critical mass on the plane	6
Bernstein type theorems of translating solitons of the mean curvature flow in higher codimension	6
Singular perturbations models in phase transitions for anisotropic higher-order materials	6
Bourgain-Brezis-Mironescu formula for $$W^{s,p}_q$$-spaces in arbitrary domains	6
Correction: Cahn–Hillard and Keller–Segel systems as high-friction limits of Euler–Korteweg and Euler–Poisson equations	6
Thermo-elastodynamics of nonlinearly viscous solids	6
Liouville type properties for a class of weighted anisotropic elliptic equations	6
$$C^{1,\alpha }$$ regularity of hypersurfaces of bounded nonlocal mean curvature in Riemannian manifolds	6
A non-local approach to the generalized Stokes operator with bounded measurable coefficients	6
Regularity for nonlocal problems with non-standard growth	6
The avoidance principle for noncompact hypersurfaces moving by mean curvature flow	6
Absence and presence of Lavrentiev’s phenomenon for double phase functionals upon every choice of exponents	6
Symmetric matrices, signed graphs, and nodal domain theorems	6
Weighted isoperimetric ratios and extension problems for fractional conformal Laplacians	6
Long time behavior for a periodic Lotka–Volterra reaction–diffusion system with strong competition	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
From almost smooth spaces to RCD spaces	5
Nonlinear Schrödinger systems with trapping potentials for mixed attractive and repulsive interactions	5
Regularity for quasi-minima of the Alt–Caffarelli functional	5
Derivation of the 1-D Groma–Balogh equations from the Peierls–Nabarro model	5
The rigidity of weighted eigenvalues on manifolds with nonnegative Ricci curvature	5
Global well-posedness of 3D homogeneous and inhomogeneous MHD system with small unidirectional derivative	5
Multiplicity of positive solutions for mixed local-nonlocal singular critical problems	5
Rigidity of min–max minimal disks in 3-balls with non-negative Ricci curvature	5
Desingularization of vortices for the incompressible Euler equation on a sphere	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
Uniqueness of Cylindrical Tangent Cones $$C_{p,q} \times \mathbb {R}$$	5
Stability of quasi-entropy solutions of non-local scalar conservation laws	5
On spin-2 Bose–Einstein condensates: classification and dynamic behavior of ground states	5
Hessian estimates for the Lagrangian mean curvature flow	5
Formation of shifted shocks for the 3D compressible Euler equations with damping	5
Quantitative estimates in elliptic homogenization of non-divergence form with unbounded drifts and an interface	5
Classification of bifurcation structure for semilinear elliptic equations in a ball	5
A variational characterization of calibrated submanifolds	5
Renormalized energy between fractional vortices with topologically induced free discontinuities on 2-dimensional Riemannian manifolds	5
A constant rank theorem for the Yamabe-type equations on locally conformally flat manifolds	5
Global solvability for a two-phase problem of inhomogeneous incompressible viscous fluids	5
Blow-up analysis and degree theory for the Webster curvature prescription problem in three dimensions	5
Glued spaces and lower Ricci curvature bounds	5
Asymptotics of the principal eigenvalue of an elliptic operator with Danckwerts boundary conditions	5
Infinite-dimensional Lipschitz stability in the Calderón problem and general Zernike bases	5
The stability of the Boltzmann equation with deformations	5
A Maupertuis-type principle in relativistic mechanics and applications	5
A planar Schrödinger–Newton system with Trudinger–Moser critical growth	5
A variational perspective on the Generalized Snell’s Law and applications to liquid crystal optics	5
Sinh-Gordon equations on finite graphs	5
Global gradient estimates for the mixed local and nonlocal problems with measurable nonlinearities	5
Existence of solutions for a system with general Hardy–Sobolev singular criticalities	4
Gelfand-type problems in random walk spaces	4
Asymptotic profiles of low-energy solutions to repulsive Schrödinger systems with critical exponents	4
Boundary plasmas for a confined plasma problem in dimensional two	4
A singular Kazdan–Warner problem on a compact Riemann surface	4
Singular solutions to the $$\sigma _k$$-Yamabe equation with prescribed asymptotics	4
Exponential decay of the solutions to nonlinear Schrödinger systems	4
The Einstein-scalar field Lichnerowicz equations on graphs	4
Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings	4
A Hardy-Hénon equation in $${\mathbb {R}}^N$$ with sublinear absorption	4
Topological degree for Chern–Simons Higgs models on finite graphs	4
Second order necessary condition for a strong minimum in the classical problem of calculus of variations	4
Global weak solutions in nonlinear 3D thermoelasticity	4
Optimal $$C^\infty $$-approximation of functions with exponentially or sub-exponentially integrable derivative	4
Multisolitons are the unique constrained minimizers of the KdV conserved quantities	4
On a sharp inequality of Adimurthi–Druet type and extremal functions	4
The half-volume spectrum of a manifold	4
Partial regularity for degenerate parabolic systems with general growth via caloric approximations	4
Global well-posedness of the 2D fractional micropolar equations	4
The structure of stable codimension one integral varifolds near classical cones of density $$Q+1/2$$	4
Fractional integration and optimal estimates for elliptic systems	4
Deformation of discrete conformal structures on surfaces	4
How far do indirect signal production mechanisms regularize the three-dimensional Keller–Segel–Stokes system?	4
Local uniqueness of blow-up solutions for critical Hartree equations in bounded domain	4
Existence and exponential stability of the global large strong solution to the 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity and large velocity	4
Dirichlet problem for Krylov type equation in conformal geometry	4
Stability of constrained solitary waves for the supercritical Kawahara equation	4
Uniqueness of hyperbolic Busemann functions in the Newtonian N-body problem	4
Regularity theory and Green’s function for elliptic equations with lower order terms in unbounded domains	4
Axisymmetric steady Navier–Stokes flows under suction	4
Li–Yau inequalities for the Helfrich functional and applications	4
Linear inverse problems with Hessian–Schatten total variation	4
Existence of periodic orbits and horseshoes for semiflows on a separable Banach space	4
Characterisation of gradient flows for a given functional	4
A systematic approach on the second order regularity of solutions to the general parabolic p-Laplace equation	4
Foliation of area minimizing hypersurfaces in asymptotically flat manifolds and Schoen’s conjecture	4
The effects of dispersal and spatial heterogeneity on the dynamics of a predator–prey model	4
Existence of singular isoperimetric regions in 8-dimensional manifolds	4
Density of Lipschitz functions in energy	4
The global curvature estimate for the $$n-2$$ Hessian equation	4
$$C^{1,{1}/{3}-}$$ very weak solutions to the two dimensional Monge–Ampère equation	4
Generalized gradient structures for measure-valued population dynamics and their large-population limit	4
Sharp uncertainty principles on metric measure spaces	4