Calculus of Variations and Partial Differential Equations

Article	Citations
Characterization of symmetric polyconvexity in higher dimensions	51
The rigidity of minimal Legendrian submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices	47
On the optimality and decay of p-Hardy weights on graphs	42
Improved regularity for the parabolic normalized p-Laplace equation	39
Trudinger–Moser and Hardy–Trudinger–Moser inequalities for the Aharonov–Bohm magnetic field	33
Concavity for elliptic and parabolic equations in locally symmetric spaces with nonnegative curvature	33
Principal spectral curves for Lane–Emden fully nonlinear type systems and applications	31
Second order $$L_p$$ estimates for subsolutions of fully nonlinear equations	29
On a novel gradient flow structure for the aggregation equation	28
Kähler Soliton Surfaces Are Generically Toric	27
Geometry of complete minimal surfaces at infinity and the Willmore index of their inversions	26
On Rabinowitz’s minimal period conjecture and subharmonic solutions for the wave equation on a disk	24
Sharp $$\textrm{L}^\infty $$ estimates for fully non-linear elliptic equations on compact complex manifolds	23
Wolff potentials and measure data vectorial problems with Orlicz growth	23
On a multi-objective control problem for the Korteweg–de Vries equation	23
Comparison theorems on H-type sub-Riemannian manifolds	20
Stable determination of an elastic medium scatterer by a single far-field measurement and beyond	20
Sharp decay estimates and asymptotic stability for incompressible MHD equations without viscosity or magnetic diffusion	19
The well-posedness of incompressible rotational jet flows with gravity	19
Hölder regularity for parabolic fractional p-Laplacian	17
Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations	17
Dichotomous concentrating solutions for a Schrödinger–Newton equation	17
Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant	17
Multi-peak solutions for semilinear elliptic equations with nearly critical Sobolev exponents in lower dimensions	16
Sharp quantitative stability of Poincaré-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows	16

Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem	16
Nonlinear stability of sinusoidal Euler flows on a flat two-torus	16
Regularity theory for non-autonomous problems with a priori assumptions	16
Optimal Hölder convergence of a class of singular steady states to the Bahouri–Chemin patch	16
Local solvability of the Poisson equation for closed $$G_2$$-structures	15
Caffarelli–Kohn–Nirenberg inequalities for curl-free vector fields and second order derivatives	15
Compactness for a class of integral functionals with interacting local and non-local terms	15
The asymptotic behavior of discrete Schrödinger equation on the hexagonal triangulation	15
On the equilibrium shape of a crystal	15
On polynomial solutions to the minimal surface equation	15
On the Yamabe invariant of certain compact manifolds with boundary	14
Hamilton-Ivey estimates for gradient Ricci solitons	14
A priori estimates and Liouville-type theorems for the semilinear parabolic equations involving the nonlinear gradient source	14
The Riemannian hemisphere is almost calibrated in the injective hull of its boundary	14
One-dimensional symmetry of positive bounded solutions to the subcubic and cubic nonlinear Schrödinger equation in the half-space in dimensions $$N=4,5$$	14
Minimisers of supremal functionals and mass-minimising 1-currents	14
Sharp anisotropic singular Trudinger–Moser inequalities in the entire space	14
Free boundary CMC annuli in spherical and hyperbolic balls	14
Variational analysis of nonlocal Dirichlet problems in periodically perforated domains	14
Scalar and mean curvature comparison via $$\mu $$-bubbles	13
Sharp estimates and non-degeneracy of low energy nodal solutions for the Lane–Emden equation in dimension two	13
Weighted fractional Poincaré inequalities via isoperimetric inequalities	13
Variational structures for the Fokker–Planck equation with general Dirichlet boundary conditions	13
On the singular planar Plateau problem	13
Convergence of semi-convex functions in CAT(1)-spaces	13
Normalized solutions for Schrödinger equations with mixed dispersion and critical exponential growth in $${\mathbb {R}}^2$$	13
Riemannian metrics with prescribed volume and finite parts of Dirichlet spectrum	13
On blow up for a class of radial Hartree type equations	13
A vectorial problem with thin free boundary	13
Steady-state Navier–Stokes flow in an obstructed pipe under mixed boundary conditions and with a prescribed transversal flux rate	12
Hypersurfaces of $$\mathbb {S}^2\times \mathbb {S}^2$$ with constant sectional curvature	12
Scattering for the non-radial inhomogenous biharmonic NLS equation	12
Front propagation and blocking of time periodic bistable reaction-diffusion equations in cylindrical domains	12
Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs	11
Blow up analysis for a parabolic MEMS problem, I: Hölder estimate	11
On functionals involving the p-capacity and the q-torsional rigidity	11
A generalization of Savin’s small perturbation theorem for fully nonlinear elliptic equations and applications	11
Local well-posedness for incompressible neo-Hookean elastic equations in almost critical Sobolev spaces	11
Brezis–Van Schaftingen–Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo–Nirenberg inequalities	10
Long time behaviour of the discrete volume preserving mean curvature flow in the flat torus	10
On the hydrostatic Navier–Stokes equations with Gevrey class 2 data	10
On the entire self-shrinking solutions to Lagrangian mean curvature flow II	10
On p-harmonic self-maps of spheres	10
Overdetermined problems for fully nonlinear equations with constant Dirichlet boundary conditions in space forms	10
Convergence of interfaces in boundary reactions	10
The $$L_{p}$$ dual Christoffel-Minkowski problem for $$1<p<q\le k+1$$ with $$1\le k\le n$$	10
$$C^\alpha $$-well-posedness of first order degenerate differential equations in banach spaces	10
Correction: a comparison principle for semilinear Hamilton–Jacobi–Bellman equations in the Wasserstein space	10
Rigidity and Łojasiewicz inequalities for Clifford self-shrinkers	10
Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group	10

Optimal coordinates for Ricci-flat conifolds	10
Symmetry of uniformly rotating solutions for the vortex-wave system	9
Boundary regularity of an isotropically censored nonlocal operator	9
Fujita-type theorems for a nonlocal quasilinear parabolic differential inequality	9
Best constants in subelliptic fractional Sobolev and Gagliardo-Nirenberg inequalities and ground states on stratified Lie groups	9
Partially regular weak solutions of the stationary Navier-Stokes equations in dimension 6	9
Some results on a gradient system with concave-convex and supercritical nonlinearities	9
Phase transition of an anisotropic Ginzburg–Landau equation	9
Nonlocal critical elliptic equations in homogeneous fractional Sobolev spaces	9
The dual $$p$$-convex functions and its applications	9
Graphical mean curvature flow with bounded bi-Ricci curvature	9
Blow up dynamics for the 3D energy-critical nonlinear Schrödinger equation	9
Local minimizers in 3d of vector Allen-Cahn with a quadruple junction.	9
From radial symmetry to fractal behavior of aggregation equilibria for repulsive–attractive potentials	9
Hardy–Sobolev interpolation inequalities	9
Global well-posedness for the Keller–Segel–Navier–Stokes system with nonlinear boundary conditions	9
Singularity Formation for the Higher Dimensional Skyrme Model	9
Uniqueness of weak solutions of the Plateau flow	9
Global dynamics of the toxicant-taxis model with Robin boundary conditions	9
Conformal Dirac–Einstein equations on manifolds with boundary.	9
Asymptotic expansions for conformal scalar curvature equations near isolated singularities	9
Blow up solutions for Sinh-Gordon equation with residual mass	9
A Liouville property for eternal solutions to a supercritical semilinear heat equation	9
Harnack’s estimate for a mixed local–nonlocal doubly nonlinear parabolic equation	8
Stationary p–harmonic maps approaching planar singular harmonic maps to the circle	8
Continuity of s-minimal functions	8
On potentials whose level sets are orbits	8
Roles of density-related diffusion and signal-dependent motilities in a chemotaxis–consumption system	8
Lusin approximation for functions of bounded variation	8
On the random G equation with nonzero divergence	8
A Cheeger inequality for the drift Laplacian with Wentzell boundary condition	8
The equality cases in Steiner’s projection inequality	8
A chemotaxis system with singular sensitivity for burglaries in the higher-dimensional settings: generalized solvability and long-time behavior	8
Dispersive estimates for Dirac Operators in dimension four with obstructions at threshold energies	8
$$L^\infty $$ continuation principle to the compressible non-isothermal nematic liquid crystal flows with zero heat conduction and vacuum	8
On the second Robin eigenvalue of the Laplacian	8
A multi-point maximum principle to prove global Harnack inequalities for Schrödinger operators	8
The spreading of global solutions of chemotaxis systems with logistic source and consumption on $$\mathbb {R}^{N}$$	8
New applications of Hadamard-in-the-mean inequalities to incompressible variational problems	8
The compressible Euler system with nonlocal pressure: global existence and relaxation	8
Rigidity and $$\varepsilon $$-regularity theorems of Ricci shrinkers	8
A universal variational framework for parabolic equations and systems	8
Quantitative stability of harmonic maps from $${\mathbb {R}}^2$$ to $${\mathbb {S}}^2$$ with a higher degree	8
On evolutionary problems with a-priori bounded gradients	8
Approaching the isoperimetric problem in $$H_{{\mathbb {C}}}^m$$ via the hyperbolic log-convex density conjecture	8
Infinitely many periodic solutions for the quasi-linear Euler–Bernoulli beam equation with fixed ends	8
Prescribing the gauss curvature of convex bodies in hyperbolic space	8
The anisotropic Gaussian isoperimetric inequality and Ehrhard symmetrization	8
Topology of complete minimal submanifolds in $${\mathbb {R}}^{n+m}$$ with finite total curvature	8
Local Lipschitz continuity of the minimizers of nonuniformly convex functionals under the Lower Bounded Slope Condition	7
A strong form of the quantitative Wulff inequality for crystalline norms	7
Homogenisation of dynamical optimal transport on periodic graphs	7
Stability of spectral partitions and the Dirichlet-to-Neumann map	7
Multiple solutions and profile description for a nonlinear Schrödinger–Bopp–Podolsky–Proca system on a manifold	7
Periodic solution for Hamiltonian type systems with critical growth	7
Surface measure on, and the local geometry of, sub-Riemannian manifolds	7
Bifurcations in Lagrangian systems and geodesics I	7
Smooth approximation of mappings with rank of the derivative at most 1	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
On nonlinear instability of liquid Lane–Emden stars	7
Manifolds for which Huber’s Theorem holds	7
Explicit forms for extremals of sharp Sobolev trace inequalities on the unit balls	7
Symmetry breaking for local minimizers of a free discontinuity problem	7
A variational characterization of calibrated submanifolds	7
Absolutely continuous and BV-curves in 1-Wasserstein spaces	7
On the free boundary problems for the ideal incompressible MHD equations	7
Prescribing negative curvature with cusps and conical singularities on compact surface	7
Higher regularity for weak solutions to degenerate parabolic problems	7
The symmetric (log-)epiperimetric inequality and a decay-growth estimate	7
Rigidity of Finsler gradient steady Ricci soliton	6
Dirichlet problem for degenerate Hessian quotient type curvature equations	6
Singular perturbations models in phase transitions for anisotropic higher-order materials	6
A Maupertuis-type principle in relativistic mechanics and applications	6
Thermo-elastodynamics of nonlinearly viscous solids	6
Absence and presence of Lavrentiev’s phenomenon for double phase functionals upon every choice of exponents	6
Regularity for nonlocal problems with non-standard growth	6
A class of fourth-order dispersive wave equations with exponential source	6
Bernstein type theorems of translating solitons of the mean curvature flow in higher codimension	6

Graphs with Lin-Lu-Yau curvature at least one and regular bone-idle graphs	6
Symmetric matrices, signed graphs, and nodal domain theorems	6
Orientability and asymptotic convergence of Q-tensor flow of biaxial nematic liquid crystals	6
On the equivalence between an Onofri-type inequality by Del Pino–Dolbeault and the sharp logarithmic Moser–Trudinger inequality	6
A planar Schrödinger–Newton system with Trudinger–Moser critical growth	6
Weighted isoperimetric ratios and extension problems for fractional conformal Laplacians	6
Quasistatic evolution in magnetoelasticity under subcritical coercivity assumptions	6
A non-local approach to the generalized Stokes operator with bounded measurable coefficients	6
Global spherically symmetric solutions to degenerate compressible Navier-Stokes equations with large data and far field vacuum	6
The existence and stability of solutions for liquid crystal two-phase interface problems	6
$$C^{1,\alpha }$$ regularity of hypersurfaces of bounded nonlocal mean curvature in Riemannian manifolds	6
The Demailly system for a direct sum of ample line bundles on Riemann surfaces	6
Nonlinear Schrödinger systems with trapping potentials for mixed attractive and repulsive interactions	6
Global well-posedness of 3D homogeneous and inhomogeneous MHD system with small unidirectional derivative	6
Bourgain-Brezis-Mironescu formula for $$W^{s,p}_q$$-spaces in arbitrary domains	6
On spin-2 Bose–Einstein condensates: classification and dynamic behavior of ground states	6
The ultimate shape of solution to the $$\varvec{L_p}$$ Minkowski problem	6
Multiplicity of positive solutions for mixed local-nonlocal singular critical problems	6
Extension operators and Korn inequality for variable coefficients in perforated domains with applications to homogenization of viscoelastic non-simple materials	6
The avoidance principle for noncompact hypersurfaces moving by mean curvature flow	6
Liouville type properties for a class of weighted anisotropic elliptic equations	6
Regularized mean curvature flow for invariant hypersurfaces in a Hilbert space and its application to gauge theory	6
Correction: Cahn–Hillard and Keller–Segel systems as high-friction limits of Euler–Korteweg and Euler–Poisson equations	6
Uniqueness of Cylindrical Tangent Cones $$C_{p,q} \times \mathbb {R}$$	5
Sinh-Gordon equations on finite graphs	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
Partial existence result for homogeneous quasilinear parabolic problems beyond the duality pairing	5
Global solvability for a two-phase problem of inhomogeneous incompressible viscous fluids	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
Blow-up analysis and degree theory for the Webster curvature prescription problem in three dimensions	5
Hessian estimates for the Lagrangian mean curvature flow	5
Asymptotics of the principal eigenvalue of an elliptic operator with Danckwerts boundary conditions	5
Glued spaces and lower Ricci curvature bounds	5
Mass, center of mass and isoperimetry in asymptotically flat 3-manifolds	5
Upper heat kernel estimates for nonlocal operators via Aronson’s method	5
On the global well-posedness and scattering of the 3D Klein–Gordon–Zakharov system	5
Planarity and convexity for pinched ancient solutions of mean curvature flow	5
A variational perspective on the Generalized Snell’s Law and applications to liquid crystal optics	5
Stability of quasi-entropy solutions of non-local scalar conservation laws	5
Global gradient estimates for the mixed local and nonlocal problems with measurable nonlinearities	5
Renormalized energy between fractional vortices with topologically induced free discontinuities on 2-dimensional Riemannian manifolds	5
The stability of the Boltzmann equation with deformations	5
Rigidity of min–max minimal disks in 3-balls with non-negative Ricci curvature	5
Formation of shifted shocks for the 3D compressible Euler equations with damping	5
Infinite-dimensional Lipschitz stability in the Calderón problem and general Zernike bases	5
Boundary plasmas for a confined plasma problem in dimensional two	5
Frankel’s property for free boundary minimal hypersurfaces in the Riemannian Schwarzschild manifolds	5
On Lipschitz Geometry at infinity of complex analytic sets	5
From almost smooth spaces to RCD spaces	5
A constant rank theorem for the Yamabe-type equations on locally conformally flat manifolds	5
Regularity for quasi-minima of the Alt–Caffarelli functional	5
Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot groups of step two	5
Quantitative estimates in elliptic homogenization of non-divergence form with unbounded drifts and an interface	5
The rigidity of weighted eigenvalues on manifolds with nonnegative Ricci curvature	5
Desingularization of vortices for the incompressible Euler equation on a sphere	5
Long time behavior for a periodic Lotka–Volterra reaction–diffusion system with strong competition	5
Derivation of the 1-D Groma–Balogh equations from the Peierls–Nabarro model	5
Scattering for three waves nonlinear Schrödinger system with mass-resonance in 5D	5
Asymptotic behavior of $$L^2$$-subcritical relativistic Fermi systems in the nonrelativistic limit	5
The global curvature estimate for the $$n-2$$ Hessian equation	4
Notes on generalized special Lagrangian equation	4
Multiple blowing-up solutions for the Choquard type Brezis-Nirenberg problem in dimension three	4
Partial regularity for degenerate parabolic systems with general growth via caloric approximations	4
Existence of periodic orbits and horseshoes for semiflows on a separable Banach space	4
The structure of stable codimension one integral varifolds near classical cones of density $$Q+1/2$$	4
A systematic approach on the second order regularity of solutions to the general parabolic p-Laplace equation	4
Fractional integration and optimal estimates for elliptic systems	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
Asymptotic profiles of low-energy solutions to repulsive Schrödinger systems with critical exponents	4
How far do indirect signal production mechanisms regularize the three-dimensional Keller–Segel–Stokes system?	4
Existence of singular isoperimetric regions in 8-dimensional manifolds	4
Global weak solutions in nonlinear 3D thermoelasticity	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
Thurston’s sphere packings on 3-dimensional manifolds, I	4
Optimal $$C^\infty $$-approximation of functions with exponentially or sub-exponentially integrable derivative	4
Local uniqueness of blow-up solutions for critical Hartree equations in bounded domain	4
Dirichlet problem for Krylov type equation in conformal geometry	4
Exponential decay of the solutions to nonlinear Schrödinger systems	4
A Hardy-Hénon equation in $${\mathbb {R}}^N$$ with sublinear absorption	4
Topological degree for Chern–Simons Higgs models on finite graphs	4
Li–Yau inequalities for the Helfrich functional and applications	4
The effects of dispersal and spatial heterogeneity on the dynamics of a predator–prey model	4
Axisymmetric steady Navier–Stokes flows under suction	4
Linear inverse problems with Hessian–Schatten total variation	4
Stability of constrained solitary waves for the supercritical Kawahara equation	4
Deformation of discrete conformal structures on surfaces	4
Improved Sobolev inequalities on CR sphere	4
Generalized gradient structures for measure-valued population dynamics and their large-population limit	4
A singular Kazdan–Warner problem on a compact Riemann surface	4
Foliation of area minimizing hypersurfaces in asymptotically flat manifolds and Schoen’s conjecture	4
$$C^{1,{1}/{3}-}$$ very weak solutions to the two dimensional Monge–Ampère equation	4
Uniqueness of hyperbolic Busemann functions in the Newtonian N-body problem	4
Density of Lipschitz functions in energy	4
The Einstein-scalar field Lichnerowicz equations on graphs	4