Calculus of Variations and Partial Differential Equations

Article	Citations
Quadratically pinched hypersurfaces of the sphere via mean curvature flow with surgery	90
The well-posedness of incompressible rotational jet flows with gravity	42
On the equilibrium shape of a crystal	38
Geometry of complete minimal surfaces at infinity and the Willmore index of their inversions	37
Sharp decay estimates and asymptotic stability for incompressible MHD equations without viscosity or magnetic diffusion	35
Characterization of symmetric polyconvexity in higher dimensions	33
The rigidity of minimal Legendrian submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices	29
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	27
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	24
Conformal tori with almost non-negative scalar curvature	22
Serrin–type regularity criteria for the 3D MHD equations via one velocity component and one magnetic component	22
Vanishing-concentration-compactness alternative for critical Sobolev embedding with a general integrand in $$\mathbb R^2$$	21
Hölder regularity for parabolic fractional p-Laplacian	20
On the optimality and decay of p-Hardy weights on graphs	19
Concavity for elliptic and parabolic equations in locally symmetric spaces with nonnegative curvature	19
Regularity theory for non-autonomous problems with a priori assumptions	19
Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant	18
On a novel gradient flow structure for the aggregation equation	18
Second order $$L_p$$ estimates for subsolutions of fully nonlinear equations	18
Nonlinear stability of sinusoidal Euler flows on a flat two-torus	17
Stable determination of an elastic medium scatterer by a single far-field measurement and beyond	17
Sharp $$\textrm{L}^\infty $$ estimates for fully non-linear elliptic equations on compact complex manifolds	17
Lower bounds for eigenvalues of Laplacian operator and the clamped plate problem	17
Comparison theorems on H-type sub-Riemannian manifolds	17

Optimal Hölder convergence of a class of singular steady states to the Bahouri–Chemin patch	16
Multi-peak solutions for semilinear elliptic equations with nearly critical Sobolev exponents in lower dimensions	16
Wolff potentials and measure data vectorial problems with Orlicz growth	16
Improved regularity for the parabolic normalized p-Laplace equation	16
Sharp quantitative stability of Poincaré-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows	15
Upper bounds for the Steklov eigenvalues on trees	15
Dichotomous concentrating solutions for a Schrödinger–Newton equation	15
Trudinger–Moser and Hardy–Trudinger–Moser inequalities for the Aharonov–Bohm magnetic field	15
Compactness for a class of integral functionals with interacting local and non-local terms	14
Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations	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
Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities	14
Scattering for the non-radial inhomogenous biharmonic NLS equation	14
A priori estimates and Liouville-type theorems for the semilinear parabolic equations involving the nonlinear gradient source	13
A vectorial problem with thin free boundary	13
Brezis–Van Schaftingen–Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo–Nirenberg inequalities	12
An Intrinsic Harnack inequality for some non-homogeneous parabolic equations in non-divergence form	12
Local boundedness for solutions of a class of nonlinear elliptic systems	12
Local solvability of the Poisson equation for closed $$G_2$$-structures	12
Minimisers of supremal functionals and mass-minimising 1-currents	12
On p-harmonic self-maps of spheres	12
Free boundary CMC annuli in spherical and hyperbolic balls	12
Existence and nonexistence in the liquid drop model	12
Normalized solutions for Schrödinger equations with mixed dispersion and critical exponential growth in $${\mathbb {R}}^2$$	12
Small order asymptotics for nonlinear fractional problems	12
Correction: a comparison principle for semilinear Hamilton–Jacobi–Bellman equations in the Wasserstein space	12
Discrete Carleman estimates and three balls inequalities	12
The Euler–Helfrich functional	11
Long time behaviour of the discrete volume preserving mean curvature flow in the flat torus	11
Weak stabilization in degenerate parabolic equations in divergence form: application to degenerate Keller–Segel systems	11
Steady-state Navier–Stokes flow in an obstructed pipe under mixed boundary conditions and with a prescribed transversal flux rate	10
Blow up analysis for a parabolic MEMS problem, I: Hölder estimate	10
Overdetermined problems for fully nonlinear equations with constant Dirichlet boundary conditions in space forms	10
Weighted fractional Poincaré inequalities via isoperimetric inequalities	10
Local well-posedness for incompressible neo-Hookean elastic equations in almost critical Sobolev spaces	10
Front propagation and blocking of time periodic bistable reaction-diffusion equations in cylindrical domains	10
Sharp estimates and non-degeneracy of low energy nodal solutions for the Lane–Emden equation in dimension two	10
On blow up for a class of radial Hartree type equations	10
Caffarelli–Kohn–Nirenberg inequalities for curl-free vector fields and second order derivatives	10
Scalar and mean curvature comparison via $$\mu $$-bubbles	10
Riemannian metrics with prescribed volume and finite parts of Dirichlet spectrum	10
Convergence of semi-convex functions in CAT(1)-spaces	10
Sharp anisotropic singular Trudinger–Moser inequalities in the entire space	10
Apriori decay estimates for Hardy–Sobolev–Maz’ya equations	10
On the singular planar Plateau problem	10
The asymptotic behavior of discrete Schrödinger equation on the hexagonal triangulation	9
Optimal coordinates for Ricci-flat conifolds	9
Hardy–Sobolev interpolation inequalities	9
Conformal Dirac–Einstein equations on manifolds with boundary.	9
Saturn ring defect around a spherical particle immersed in a nematic liquid crystal	9

Hypersurfaces of $$\mathbb {S}^2\times \mathbb {S}^2$$ with constant sectional curvature	9
Rigidity and Łojasiewicz inequalities for Clifford self-shrinkers	9
On the entire self-shrinking solutions to Lagrangian mean curvature flow II	9
Boundary regularity of an isotropically censored nonlocal operator	9
Isoperimetric inequalities and geometry of level curves of harmonic functions on smooth and singular surfaces	9
Normalized multi-bump solutions of nonlinear Schrödinger equations via variational approach	9
Convergence of interfaces in boundary reactions	9
Uniqueness of weak solutions of the Plateau flow	9
Regularity estimates for fully nonlinear elliptic PDEs with general Hamiltonian terms and unbounded ingredients	9
Fujita-type theorems for a nonlocal quasilinear parabolic differential inequality	9
From radial symmetry to fractal behavior of aggregation equilibria for repulsive–attractive potentials	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
On rectifiable measures in Carnot groups: representation	8
On convex functions and elliptic operators	8
On potentials whose level sets are orbits	8
On the hydrostatic Navier–Stokes equations with Gevrey class 2 data	8
Approaching the isoperimetric problem in $$H_{{\mathbb {C}}}^m$$ via the hyperbolic log-convex density conjecture	8
On evolutionary problems with a-priori bounded gradients	8
Partially regular weak solutions of the stationary Navier-Stokes equations in dimension 6	8
The dual $$p$$-convex functions and its applications	8
On the two dimensional fast phase transition equation: well-posedness and long-time dynamics	8
Phase transition of an anisotropic Ginzburg–Landau equation	8
Blow up solutions for Sinh-Gordon equation with residual mass	8
On the second Robin eigenvalue of the Laplacian	8
Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group	8
Graphical mean curvature flow with bounded bi-Ricci curvature	8
A chemotaxis system with singular sensitivity for burglaries in the higher-dimensional settings: generalized solvability and long-time behavior	8
A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers	8
Manifolds for which Huber’s Theorem holds	7
The compressible Euler system with nonlocal pressure: global existence and relaxation	7
Roles of density-related diffusion and signal-dependent motilities in a chemotaxis–consumption system	7
On nonlinear instability of liquid Lane–Emden stars	7
The anisotropic Gaussian isoperimetric inequality and Ehrhard symmetrization	7
Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast	7
Augmented Lagrangian methods for degenerate Hamilton–Jacobi equations	7
A free boundary isometric embedding problem in the unit ball	7
Absolutely continuous and BV-curves in 1-Wasserstein spaces	7
A universal variational framework for parabolic equations and systems	7
Harnack’s estimate for a mixed local–nonlocal doubly nonlinear parabolic equation	7
Rigidity and $$\varepsilon $$-regularity theorems of Ricci shrinkers	7
Existence of minimizers for causal variational principles on compact subsets of momentum space in the homogeneous setting	7
Prescribing the gauss curvature of convex bodies in hyperbolic space	7
Multiple solutions and profile description for a nonlinear Schrödinger–Bopp–Podolsky–Proca system on a manifold	7
Hardy and Rellich inequality on lattices	7
Surface measure on, and the local geometry of, sub-Riemannian manifolds	7
$$L^\infty $$ continuation principle to the compressible non-isothermal nematic liquid crystal flows with zero heat conduction and vacuum	7
Continuity of s-minimal functions	7
Explicit forms for extremals of sharp Sobolev trace inequalities on the unit balls	7
Higher regularity for weak solutions to degenerate parabolic problems	7
On the random G equation with nonzero divergence	7
The equality cases in Steiner’s projection inequality	7
A Maupertuis-type principle in relativistic mechanics and applications	6
Periodic solution for Hamiltonian type systems with critical growth	6
The symmetric (log-)epiperimetric inequality and a decay-growth estimate	6
On the free boundary problems for the ideal incompressible MHD equations	6
The avoidance principle for noncompact hypersurfaces moving by mean curvature flow	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
Blow-up solutions for a system of Schrödinger equations with general quadratic-type nonlinearities in dimensions five and six	6
Mixed boundary valued problems for linear and nonlinear wave equations in domains with fractal boundaries	6
Convergence rates for the Allen–Cahn equation with boundary contact energy: the non-perturbative regime	6
Stability of spectral partitions and the Dirichlet-to-Neumann map	6
Homogenisation of dynamical optimal transport on periodic graphs	6
The Demailly system for a direct sum of ample line bundles on Riemann surfaces	6
A strong form of the quantitative Wulff inequality for crystalline norms	6
Prescribing discrete Gaussian curvature on polyhedral surfaces	6
Local behavior of positive solutions of higher order conformally invariant equations with a singular set	6
Symmetric matrices, signed graphs, and nodal domain theorems	6
Smooth approximation of mappings with rank of the derivative at most 1	6
Lusin approximation for functions of bounded variation	6
The spreading of global solutions of chemotaxis systems with logistic source and consumption on $$\mathbb {R}^{N}$$	6
A variational characterization of calibrated submanifolds	6
Regularized mean curvature flow for invariant hypersurfaces in a Hilbert space and its application to gauge theory	6
Global spherically symmetric solutions to degenerate compressible Navier-Stokes equations with large data and far field vacuum	6
Bernstein type theorems of translating solitons of the mean curvature flow in higher codimension	6
On the equivalence between an Onofri-type inequality by Del Pino–Dolbeault and the sharp logarithmic Moser–Trudinger inequality	6
Bourgain-Brezis-Mironescu formula for $$W^{s,p}_q$$-spaces in arbitrary domains	5
Derivation of the 1-D Groma–Balogh equations from the Peierls–Nabarro model	5
Some elliptic problems involving the gradient on general bounded and exterior domains	5

Regularity for quasi-minima of the Alt–Caffarelli functional	5
Long time behavior for a periodic Lotka–Volterra reaction–diffusion system with strong competition	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
Stability of quasi-entropy solutions of non-local scalar conservation laws	5
Bubbling phenomenon for semilinear Neumann elliptic equations of critical exponential growth	5
Dirichlet problem for degenerate Hessian quotient type curvature equations	5
Scattering for three waves nonlinear Schrödinger system with mass-resonance in 5D	5
Multiplicity of positive solutions for mixed local-nonlocal singular critical problems	5
Asymptotic behavior of $$L^2$$-subcritical relativistic Fermi systems in the nonrelativistic limit	5
Rigidity of Finsler gradient steady Ricci soliton	5
Boundary plasmas for a confined plasma problem in dimensional two	5
Graphs with Lin-Lu-Yau curvature at least one and regular bone-idle graphs	5
Quantitative estimates in elliptic homogenization of non-divergence form with unbounded drifts and an interface	5
Extension operators and Korn inequality for variable coefficients in perforated domains with applications to homogenization of viscoelastic non-simple materials	5
Asymptotics of the principal eigenvalue of an elliptic operator with Danckwerts boundary conditions	5
A class of fourth-order dispersive wave equations with exponential source	5
Partial existence result for homogeneous quasilinear parabolic problems beyond the duality pairing	5
Regularity for nonlocal problems with non-standard growth	5
Traveling vortex pairs for 2D incompressible Euler equations	5
Transition fronts of combustion reaction–diffusion equations around an obstacle	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
Mass, center of mass and isoperimetry in asymptotically flat 3-manifolds	5
Orientability and asymptotic convergence of Q-tensor flow of biaxial nematic liquid crystals	5
Notes on generalized special Lagrangian equation	5
Renormalized energy between fractional vortices with topologically induced free discontinuities on 2-dimensional Riemannian manifolds	5
Infinitely many nodal solutions of Kirchhoff-type equations with asymptotically cubic nonlinearity without oddness hypothesis	5
Perturbed Schrödinger lattice systems with superlinear terms: Multiplicity of homoclinic solutions	5
Harnack inequality for nonlocal operators on manifolds with nonnegative curvature	5
A planar Schrödinger–Newton system with Trudinger–Moser critical growth	5
Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot groups of step two	5
Correction: Cahn–Hillard and Keller–Segel systems as high-friction limits of Euler–Korteweg and Euler–Poisson equations	5
Global gradient estimates for the mixed local and nonlocal problems with measurable nonlinearities	5
Quasistatic evolution in magnetoelasticity under subcritical coercivity assumptions	5
Correction to: Two generalized Tricomi equations	5
Global well-posedness of 3D homogeneous and inhomogeneous MHD system with small unidirectional derivative	5
Hessian estimates for the Lagrangian mean curvature flow	5
Volume comparison theorem with respect to sigma-k curvature	5
Unbounded mass radial solutions for the Keller–Segel equation in the disk	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
Nonlinear Schrödinger systems with trapping potentials for mixed attractive and repulsive interactions	5
Frankel’s property for free boundary minimal hypersurfaces in the Riemannian Schwarzschild manifolds	5
Non-minimality of spirals in sub-Riemannian manifolds	5
On the global well-posedness and scattering of the 3D Klein–Gordon–Zakharov system	5
Variational aspects of phase transitions with prescribed mean curvature	5
Volume minimising unit vector fields on three dimensional space forms of positive curvature	5
Absence and presence of Lavrentiev’s phenomenon for double phase functionals upon every choice of exponents	5
Prescribed mass standing waves for energy critical Hartree equations	4
EDP-convergence for a linear reaction-diffusion system with fast reversible reaction	4
Regularity for quasi-linear parabolic equations with nonhomogeneous degeneracy or singularity	4
Deformations of Q-curvature II	4
Harnack-type estimates and extinction in finite time for a class of anisotropic porous medium type equations	4
Exponential decay of the solutions to nonlinear Schrödinger systems	4
Upper heat kernel estimates for nonlocal operators via Aronson’s method	4
Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings	4
Gelfand-type problems in random walk spaces	4
How far do indirect signal production mechanisms regularize the three-dimensional Keller–Segel–Stokes system?	4
The Einstein-scalar field Lichnerowicz equations on graphs	4
Curvature estimates for semi-convex solutions of Hessian equations in hyperbolic space	4
The global curvature estimate for the $$n-2$$ Hessian equation	4
Representation formulas and pointwise properties for Barron functions	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
A singular Kazdan–Warner problem on a compact Riemann surface	4
Fractional integration and optimal estimates for elliptic systems	4
The effects of dispersal and spatial heterogeneity on the dynamics of a predator–prey model	4
Existence of ground state solutions to some Nonlinear Schrödinger equations on lattice graphs	4
The structure of stable codimension one integral varifolds near classical cones of density $$Q+1/2$$	4
On Lipschitz Geometry at infinity of complex analytic sets	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
Regularity theory and Green’s function for elliptic equations with lower order terms in unbounded domains	4
Non-uniqueness in law for the Boussinesq system forced by random noise	4
Linear inverse problems with Hessian–Schatten total variation	4
Topological degree for Chern–Simons Higgs models on finite graphs	4
Generalized gradient structures for measure-valued population dynamics and their large-population limit	4
A Hardy-Hénon equation in $${\mathbb {R}}^N$$ with sublinear absorption	4
Existence of solutions for a system with general Hardy–Sobolev singular criticalities	4
Sharp uncertainty principles on metric measure spaces	4
Existence of periodic orbits and horseshoes for semiflows on a separable Banach space	4
Singular solutions to the $$\sigma _k$$-Yamabe equation with prescribed asymptotics	4
Partial regularity for degenerate parabolic systems with general growth via caloric approximations	4
Axisymmetric steady Navier–Stokes flows under suction	4
On a sharp inequality of Adimurthi–Druet type and extremal functions	4
Radial symmetry of solutions to anisotropic and weighted diffusion equations with discontinuous nonlinearities	4
Density of Lipschitz functions in energy	4
Entire solutions to the Swift–Hohenberg equation via a variational approach	4
Li–Yau inequalities for the Helfrich functional and applications	4
The half-volume spectrum of a manifold	4
Characterisation of gradient flows for a given functional	4
Existence of singular isoperimetric regions in 8-dimensional manifolds	4
Global weak solutions in nonlinear 3D thermoelasticity	4
$$C^{1,{1}/{3}-}$$ very weak solutions to the two dimensional Monge–Ampère equation	4
Deformation of discrete conformal structures on surfaces	4
A systematic approach on the second order regularity of solutions to the general parabolic p-Laplace equation	4