Calculus of Variations and Partial Differential Equations

Article	Citations
Geometry of complete minimal surfaces at infinity and the Willmore index of their inversions	47
Sharp decay estimates and asymptotic stability for incompressible MHD equations without viscosity or magnetic diffusion	44
The rigidity of minimal Legendrian submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices	43
Characterization of symmetric polyconvexity in higher dimensions	43
Sharp $$\textrm{L}^\infty $$ estimates for fully non-linear elliptic equations on compact complex manifolds	35
Conformal tori with almost non-negative scalar curvature	31
Trudinger–Moser and Hardy–Trudinger–Moser inequalities for the Aharonov–Bohm magnetic field	29
Comparison theorems on H-type sub-Riemannian manifolds	28
Optimal Hölder convergence of a class of singular steady states to the Bahouri–Chemin patch	27
Stable determination of an elastic medium scatterer by a single far-field measurement and beyond	24
On the equilibrium shape of a crystal	24
Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant	23
On a novel gradient flow structure for the aggregation equation	22
Second order $$L_p$$ estimates for subsolutions of fully nonlinear equations	22
Nonlinear stability of sinusoidal Euler flows on a flat two-torus	22
Serrin–type regularity criteria for the 3D MHD equations via one velocity component and one magnetic component	21
Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem	21
Kähler Soliton Surfaces Are Generically Toric	21
Multi-peak solutions for semilinear elliptic equations with nearly critical Sobolev exponents in lower dimensions	21
Concavity for elliptic and parabolic equations in locally symmetric spaces with nonnegative curvature	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	19
Principal spectral curves for Lane–Emden fully nonlinear type systems and applications	19
Upper bounds for the Steklov eigenvalues on trees	18
Improved regularity for the parabolic normalized p-Laplace equation	18
Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities	18

Sharp quantitative stability of Poincaré-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows	18
Dichotomous concentrating solutions for a Schrödinger–Newton equation	17
Wolff potentials and measure data vectorial problems with Orlicz growth	17
Regularity theory for non-autonomous problems with a priori assumptions	16
On the optimality and decay of p-Hardy weights on graphs	16
Hölder regularity for parabolic fractional p-Laplacian	16
On a multi-objective control problem for the Korteweg–de Vries equation	16
The asymptotic behavior of discrete Schrödinger equation on the hexagonal triangulation	15
Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations	15
Compactness for a class of integral functionals with interacting local and non-local terms	15
The well-posedness of incompressible rotational jet flows with gravity	15
Local solvability of the Poisson equation for closed $$G_2$$-structures	15
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
Sharp anisotropic singular Trudinger–Moser inequalities in the entire space	13
On blow up for a class of radial Hartree type equations	13
Sharp estimates and non-degeneracy of low energy nodal solutions for the Lane–Emden equation in dimension two	13
Scattering for the non-radial inhomogenous biharmonic NLS equation	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	13
Overdetermined problems for fully nonlinear equations with constant Dirichlet boundary conditions in space forms	13
Blow up analysis for a parabolic MEMS problem, I: Hölder estimate	13
Correction: a comparison principle for semilinear Hamilton–Jacobi–Bellman equations in the Wasserstein space	13
Long time behaviour of the discrete volume preserving mean curvature flow in the flat torus	13
The Euler–Helfrich functional	13
Convergence of semi-convex functions in CAT(1)-spaces	13
Riemannian metrics with prescribed volume and finite parts of Dirichlet spectrum	13
One-dimensional symmetry of positive bounded solutions to the subcubic and cubic nonlinear Schrödinger equation in the half-space in dimensions $$N=4,5$$	13
On the singular planar Plateau problem	12
Hypersurfaces of $$\mathbb {S}^2\times \mathbb {S}^2$$ with constant sectional curvature	12
On p-harmonic self-maps of spheres	12
Weighted fractional Poincaré inequalities via isoperimetric inequalities	12
Local well-posedness for incompressible neo-Hookean elastic equations in almost critical Sobolev spaces	12
Brezis–Van Schaftingen–Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo–Nirenberg inequalities	11
The Riemannian hemisphere is almost calibrated in the injective hull of its boundary	11
Minimisers of supremal functionals and mass-minimising 1-currents	11
Local boundedness for solutions of a class of nonlinear elliptic systems	11
On functionals involving the p-capacity and the q-torsional rigidity	11
Hamilton-Ivey estimates for gradient Ricci solitons	11
On the Yamabe invariant of certain compact manifolds with boundary	11
Free boundary CMC annuli in spherical and hyperbolic balls	11
Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs	11
Variational structures for the Fokker–Planck equation with general Dirichlet boundary conditions	11
Variational analysis of nonlocal Dirichlet problems in periodically perforated domains	10
Small order asymptotics for nonlinear fractional problems	10
On the hydrostatic Navier–Stokes equations with Gevrey class 2 data	10
Phase transition of an anisotropic Ginzburg–Landau equation	10
Optimal coordinates for Ricci-flat conifolds	10
Caffarelli–Kohn–Nirenberg inequalities for curl-free vector fields and second order derivatives	10
Front propagation and blocking of time periodic bistable reaction-diffusion equations in cylindrical domains	10

Scalar and mean curvature comparison via $$\mu $$-bubbles	10
Convergence of interfaces in boundary reactions	10
On the entire self-shrinking solutions to Lagrangian mean curvature flow II	10
Normalized solutions for Schrödinger equations with mixed dispersion and critical exponential growth in $${\mathbb {R}}^2$$	10
Weak stabilization in degenerate parabolic equations in divergence form: application to degenerate Keller–Segel systems	10
Rigidity and Łojasiewicz inequalities for Clifford self-shrinkers	10
Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group	10
The $$L_{p}$$ dual Christoffel-Minkowski problem for $$1<p<q\le k+1$$ with $$1\le k\le n$$	10
Symmetry of uniformly rotating solutions for the vortex-wave system	9
Global dynamics of the toxicant-taxis model with Robin boundary conditions	9
Hardy–Sobolev interpolation inequalities	9
Uniqueness of weak solutions of the Plateau flow	9
Partially regular weak solutions of the stationary Navier-Stokes equations in dimension 6	9
Normalized multi-bump solutions of nonlinear Schrödinger equations via variational approach	9
Nonlocal critical elliptic equations in homogeneous fractional Sobolev spaces	9
Best constants in subelliptic fractional Sobolev and Gagliardo-Nirenberg inequalities and ground states on stratified Lie groups	9
From radial symmetry to fractal behavior of aggregation equilibria for repulsive–attractive potentials	9
Conformal Dirac–Einstein equations on manifolds with boundary.	9
The dual $$p$$-convex functions and its applications	9
Global well-posedness for the Keller–Segel–Navier–Stokes system with nonlinear boundary conditions	9
Graphical mean curvature flow with bounded bi-Ricci curvature	9
Some results on a gradient system with concave-convex and supercritical nonlinearities	9
Fujita-type theorems for a nonlocal quasilinear parabolic differential inequality	9
Boundary regularity of an isotropically censored nonlocal operator	9
On convex functions and elliptic operators	9
Singularity Formation for the Higher Dimensional Skyrme Model	9
Continuity of s-minimal functions	8
Infinitely many periodic solutions for the quasi-linear Euler–Bernoulli beam equation with fixed ends	8
Manifolds for which Huber’s Theorem holds	8
Harnack’s estimate for a mixed local–nonlocal doubly nonlinear parabolic equation	8
On potentials whose level sets are orbits	8
Quantitative stability of harmonic maps from $${\mathbb {R}}^2$$ to $${\mathbb {S}}^2$$ with a higher degree	8
Dispersive estimates for Dirac Operators in dimension four with obstructions at threshold energies	8
The compressible Euler system with nonlocal pressure: global existence and relaxation	8
Rigidity and $$\varepsilon $$-regularity theorems of Ricci shrinkers	8
On the second Robin eigenvalue of the Laplacian	8
Stationary p–harmonic maps approaching planar singular harmonic maps to the circle	8
On evolutionary problems with a-priori bounded gradients	8
$$L^\infty $$ continuation principle to the compressible non-isothermal nematic liquid crystal flows with zero heat conduction and vacuum	8
A universal variational framework for parabolic equations and systems	8
Explicit forms for extremals of sharp Sobolev trace inequalities on the unit balls	8
A chemotaxis system with singular sensitivity for burglaries in the higher-dimensional settings: generalized solvability and long-time behavior	8
Roles of density-related diffusion and signal-dependent motilities in a chemotaxis–consumption system	8
Blow up solutions for Sinh-Gordon equation with residual mass	8
Approaching the isoperimetric problem in $$H_{{\mathbb {C}}}^m$$ via the hyperbolic log-convex density conjecture	8
Lusin approximation for functions of bounded variation	7
Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast	7
A free boundary isometric embedding problem in the unit ball	7
Stability of spectral partitions and the Dirichlet-to-Neumann map	7
Homogenisation of dynamical optimal transport on periodic graphs	7
Mixed boundary valued problems for linear and nonlinear wave equations in domains with fractal boundaries	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
New applications of Hadamard-in-the-mean inequalities to incompressible variational problems	7
Prescribing the gauss curvature of convex bodies in hyperbolic space	7
Existence of minimizers for causal variational principles on compact subsets of momentum space in the homogeneous setting	7
On the random G equation with nonzero divergence	7
Absolutely continuous and BV-curves in 1-Wasserstein spaces	7
Prescribing discrete Gaussian curvature on polyhedral surfaces	7
On the free boundary problems for the ideal incompressible MHD equations	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
The equality cases in Steiner’s projection inequality	7
The anisotropic Gaussian isoperimetric inequality and Ehrhard symmetrization	7
The spreading of global solutions of chemotaxis systems with logistic source and consumption on $$\mathbb {R}^{N}$$	7
Smooth approximation of mappings with rank of the derivative at most 1	7
Hardy and Rellich inequality on lattices	7
A Maupertuis-type principle in relativistic mechanics and applications	7
On nonlinear instability of liquid Lane–Emden stars	7
Extension operators and Korn inequality for variable coefficients in perforated domains with applications to homogenization of viscoelastic non-simple materials	6
Variational aspects of phase transitions with prescribed mean curvature	6
Global spherically symmetric solutions to degenerate compressible Navier-Stokes equations with large data and far field vacuum	6
The Demailly system for a direct sum of ample line bundles on Riemann surfaces	6
Blow-up solutions for a system of Schrödinger equations with general quadratic-type nonlinearities in dimensions five and six	6
Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot groups of step two	6
Low Mach number limit for the global large solutions to the 2D Navier–Stokes–Korteweg system in the critical $$\widehat{L^p}$$ framework	6
A planar Schrödinger–Newton system with Trudinger–Moser critical growth	6
Regularity for nonlocal problems with non-standard growth	6

Singular perturbations models in phase transitions for anisotropic higher-order materials	6
Liouville type properties for a class of weighted anisotropic elliptic equations	6
A variational characterization of calibrated submanifolds	6
On the equivalence between an Onofri-type inequality by Del Pino–Dolbeault and the sharp logarithmic Moser–Trudinger inequality	6
A strong form of the quantitative Wulff inequality for crystalline norms	6
The avoidance principle for noncompact hypersurfaces moving by mean curvature flow	6
Bourgain-Brezis-Mironescu formula for $$W^{s,p}_q$$-spaces in arbitrary domains	6
The existence and stability of solutions for liquid crystal two-phase interface problems	6
Orientability and asymptotic convergence of Q-tensor flow of biaxial nematic liquid crystals	6
Stability of quasi-entropy solutions of non-local scalar conservation laws	6
Absence and presence of Lavrentiev’s phenomenon for double phase functionals upon every choice of exponents	6
Multiplicity of positive solutions for mixed local-nonlocal singular critical problems	6
Graphs with Lin-Lu-Yau curvature at least one and regular bone-idle graphs	6
Regularized mean curvature flow for invariant hypersurfaces in a Hilbert space and its application to gauge theory	6
$$C^{1,\alpha }$$ regularity of hypersurfaces of bounded nonlocal mean curvature in Riemannian manifolds	6
Symmetric matrices, signed graphs, and nodal domain theorems	6
Bernstein type theorems of translating solitons of the mean curvature flow in higher codimension	6
Rigidity of Finsler gradient steady Ricci soliton	6
Global well-posedness of 3D homogeneous and inhomogeneous MHD system with small unidirectional derivative	6
Quasistatic evolution in magnetoelasticity under subcritical coercivity assumptions	6
A class of fourth-order dispersive wave equations with exponential source	6
Correction: Cahn–Hillard and Keller–Segel systems as high-friction limits of Euler–Korteweg and Euler–Poisson equations	6
Long time behavior for a periodic Lotka–Volterra reaction–diffusion system with strong competition	5
Scattering for three waves nonlinear Schrödinger system with mass-resonance in 5D	5
On the global well-posedness and scattering of the 3D Klein–Gordon–Zakharov system	5
Gelfand-type problems in random walk spaces	5
Volume minimising unit vector fields on three dimensional space forms of positive curvature	5
Axisymmetric steady Navier–Stokes flows under suction	5
Derivation of the 1-D Groma–Balogh equations from the Peierls–Nabarro model	5
Boundary plasmas for a confined plasma problem in dimensional two	5
Renormalized energy between fractional vortices with topologically induced free discontinuities on 2-dimensional Riemannian manifolds	5
Frankel’s property for free boundary minimal hypersurfaces in the Riemannian Schwarzschild manifolds	5
Blow-up analysis and degree theory for the Webster curvature prescription problem in three dimensions	5
The rigidity of weighted eigenvalues on manifolds with nonnegative Ricci curvature	5
Rigidity of min–max minimal disks in 3-balls with non-negative Ricci curvature	5
On spin-2 Bose–Einstein condensates: classification and dynamic behavior of ground states	5
Asymptotics of the principal eigenvalue of an elliptic operator with Danckwerts boundary conditions	5
Infinitely many nodal solutions of Kirchhoff-type equations with asymptotically cubic nonlinearity without oddness hypothesis	5
Bubbling phenomenon for semilinear Neumann elliptic equations of critical exponential growth	5
Entire solutions to the Swift–Hohenberg equation via a variational approach	5
Non-uniqueness in law for the Boussinesq system forced by random noise	5
Harnack-type estimates and extinction in finite time for a class of anisotropic porous medium type equations	5
Global gradient estimates for the mixed local and nonlocal problems with measurable nonlinearities	5
Upper heat kernel estimates for nonlocal operators via Aronson’s method	5
Global solvability for a two-phase problem of inhomogeneous incompressible viscous fluids	5
The stability of the Boltzmann equation with deformations	5
Asymptotic behavior of $$L^2$$-subcritical relativistic Fermi systems in the nonrelativistic limit	5
Hessian estimates for the Lagrangian mean curvature flow	5
Sinh-Gordon equations on finite graphs	5
Dirichlet problem for degenerate Hessian quotient type curvature equations	5
Partial existence result for homogeneous quasilinear parabolic problems beyond the duality pairing	5
Linear inverse problems with Hessian–Schatten total variation	5
The half-volume spectrum of a manifold	5
Existence of ground state solutions to some Nonlinear Schrödinger equations on lattice graphs	5
Prescribed mass standing waves for energy critical Hartree 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
Mass, center of mass and isoperimetry in asymptotically flat 3-manifolds	5
Regularity for quasi-minima of the Alt–Caffarelli functional	5
On Lipschitz Geometry at infinity of complex analytic sets	5
Formation of shifted shocks for the 3D compressible Euler equations with damping	5
Desingularization of vortices for the incompressible Euler equation on a sphere	5
Volume comparison theorem with respect to sigma-k curvature	5
Quantitative estimates in elliptic homogenization of non-divergence form with unbounded drifts and an interface	5
Nonlinear Schrödinger systems with trapping potentials for mixed attractive and repulsive interactions	5
Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids	4
The Dirichlet-to-Neumann operator associated with the 1-Laplacian and evolution problems	4
Asymptotic profiles of low-energy solutions to repulsive Schrödinger systems with critical exponents	4
Fractional integration and optimal estimates for elliptic systems	4
How far do indirect signal production mechanisms regularize the three-dimensional Keller–Segel–Stokes system?	4
Partial regularity for degenerate parabolic systems with general growth via caloric approximations	4
A singular Kazdan–Warner problem on a compact Riemann surface	4
On the structure of weak solutions to scalar conservation laws with finite entropy production	4
Gradient flow solutions for porous medium equations with nonlocal Lévy-type pressure	4
Weight metamorphosis of varifolds and the LDDMM-Fisher-Rao metric	4
Thurston’s sphere packings on 3-dimensional manifolds, I	4
Existence of singular isoperimetric regions in 8-dimensional manifolds	4
A Hardy-Hénon equation in $${\mathbb {R}}^N$$ with sublinear absorption	4
Density of Lipschitz functions in energy	4
The global curvature estimate for the $$n-2$$ Hessian equation	4
Li–Yau inequalities for the Helfrich functional and applications	4
Local uniqueness of blow-up solutions for critical Hartree equations in bounded domain	4
Almost-Riemannian manifolds do not satisfy the curvature-dimension condition	4
Almost minimizers for a sublinear system with free boundary	4
Palais–Smale sequences for the prescribed Ricci curvature functional	4
The nodal set of solutions to some nonlocal sublinear problems	4
Compactness and existence results of the prescribing fractional Q-curvature problem on $$\mathbb {S}^n$$	4
Improved Sobolev inequalities on CR sphere	4
Deformation of discrete conformal structures on surfaces	4
Stability of constrained solitary waves for the supercritical Kawahara equation	4
Global weak solutions in nonlinear 3D thermoelasticity	4
Topological degree for Chern–Simons Higgs models on finite graphs	4
Examples for scalar sphere stability	4
On bifurcation from infinity: a compactification approach	4
Fractional higher order thin film equation with linear mobility: gradient flow approach	4
Yamabe flow and locally conformally flat manifolds with positive pinched Ricci curvature	4