Calculus of Variations and Partial Differential Equations

Article	Citations
Normalized solutions for a Schrödinger equation with critical growth in $${\mathbb {R}}^{N}$$	61
Comparison methods for a Keller–Segel-type model of pattern formations with density-suppressed motilities	58
Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities	29
Characterisation of homogeneous fractional Sobolev spaces	29
Existence of normalized ground states for the Sobolev critical Schrödinger equation with combined nonlinearities	28
Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy	25
Multiplicity results for (p, q)-Laplacian equations with critical exponent in $${\mathbb {R}}^N$$ and negative energy	24
Concentration behavior of endemic equilibrium for a reaction–diffusion–advection SIS epidemic model with mass action infection mechanism	24
Stability and exponential decay for the 2D anisotropic Boussinesq equations with horizontal dissipation	24
Eventual smoothness and stabilization in a three-dimensional Keller–Segel–Navier–Stokes system with rotational flux	24
On a planar non-autonomous Schrödinger–Poisson system involving exponential critical growth	23
Limiting behavior and local uniqueness of normalized solutions for mass critical Kirchhoff equations	23
On global minimizers for a mass constrained problem	21
Local boundedness and Hölder continuity for the parabolic fractional p-Laplace equations	21
Schrödinger–Newton equations in dimension two via a Pohozaev–Trudinger log-weighted inequality	20
Sobolev and Hölder regularity results for some singular nonhomogeneous quasilinear problems	20
Saddle solutions for the critical Choquard equation	19
Asymptotic behavior of a quasilinear Keller–Segel system with signal-suppressed motility	18
A blow-up result for a semilinear wave equation with scale-invariant damping and mass and nonlinearity of derivative type	18
Mean field games with state constraints: from mild to pointwise solutions of the PDE system	18
$$\Gamma $$-convergence of polyconvex functionals involving s-fractional gradients to their local counterparts	18
Least energy solutions to a cooperative system of Schrödinger equations with prescribed $$L^2$$-bounds: at least $$L^2$$-critical growth	17
Global well-posedness for a class of semilinear hyperbolic equations with singular potentials on manifolds with conical singularities	17
Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations	17
A heat flow for the mean field equation on a finite graph	17

Entire solutions of time periodic bistable Lotka–Volterra competition-diffusion systems in $${\mathbb {R}}^N$$	16
On the planar Schrödinger equation with indefinite linear part and critical growth nonlinearity	16
Curvature estimates for a class of Hessian type equations	15
Well-posedness of the two-dimensional Abels–Garcke–Grün model for two-phase flows with unmatched densities	15
Higher integrability for variational integrals with non-standard growth	15
Brezis–Van Schaftingen–Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo–Nirenberg inequalities	15
A nonlocal isoperimetric problem with density perimeter	15
The fractional p-Laplacian evolution equation in $${\mathbb {R}}^N$$ in the sublinear case	14
Global higher integrability for minimisers of convex functionals with (p,q)-growth	14
Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail	14
Excited states of Bose–Einstein condensates with degenerate attractive interactions	14
Higher Hölder regularity for nonlocal equations with irregular kernel	13
Monotonicity-based inversion of fractional semilinear elliptic equations with power type nonlinearities	13
The structure of the singular set in the thin obstacle problem for degenerate parabolic equations	13
Global existence and convergence of a flow to Kazdan–Warner equation with non-negative prescribed function	13
Jump processes as generalized gradient flows	13
Critical Stein–Weiss elliptic systems: symmetry, regularity and asymptotic properties of solutions	13
Martin kernel of Schrödinger operators with singular potentials and applications to B.V.P. for linear elliptic equations	12
Regularity for parabolic equations with singular or degenerate coefficients	12
New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems	12
Korevaar–Schoen’s energy on strongly rectifiable spaces	12
On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth	12
Sharp patterns of positive solutions for some weighted semilinear elliptic problems	12
On the Brezis–Nirenberg problem for a Kirchhoff type equation in high dimension	12
Ground states for the planar NLSE with a point defect as minimizers of the constrained energy	12
Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates	12
Radial symmetry of solutions to anisotropic and weighted diffusion equations with discontinuous nonlinearities	12
Blow-up solutions to the Monge–Ampère equation with a gradient term: sharp conditions for the existence and asymptotic estimates	11
Local Hölder regularity for nonlocal equations with variable powers	11
Gradient estimates for multi-phase problems	11
Regularity for nonlocal problems with non-standard growth	11
The equilibrium measure for an anisotropic nonlocal energy	11
Existence of solutions to Chern–Simons–Higgs equations on graphs	11
The $$L_p$$-Gaussian Minkowski problem	11
Existence and symmetry breaking of ground state solutions for Schrödinger–Poisson systems	11
On rectifiable measures in Carnot groups: representation	11
Stable determination of an elastic medium scatterer by a single far-field measurement and beyond	11
Construction of infinitely many solutions for a critical Choquard equation via local Pohožaev identities	10
A planar Schrödinger–Newton system with Trudinger–Moser critical growth	10
The Łojasiewicz–Simon inequality for the elastic flow	10
Rigidity and almost rigidity of Sobolev inequalities on compact spaces with lower Ricci curvature bounds	10
Prescribed signal concentration on the boundary: eventual smoothness in a chemotaxis-Navier–Stokes system with logistic proliferation	10
A theory of spectral partitions of metric graphs	10
Orlicz–Minkowski flows	10
Global higher integrability for minimisers of convex obstacle problems with (p,q)-growth	10
Optimal decay for the 3D anisotropic Boussinesq equations near the hydrostatic balance	9
Traveling vortex pairs for 2D incompressible Euler equations	9
Global well-posedness to the 2D Cauchy problem of nonhomogeneous heat conducting magnetohydrodynamic equations with large initial data and vacuum	9
Classification of anti-symmetric solutions to nonlinear fractional Laplace equations	9
Existence of ground state solutions to some Nonlinear Schrödinger equations on lattice graphs	9

Positive energy static solutions for the Chern–Simons–Schrödinger system under a large-distance fall-off requirement on the gauge potentials	9
Noncoercive quasilinear elliptic operators with singular lower order terms	9
On global solutions to a viscous compressible two-fluid model with unconstrained transition to single-phase flow in three dimensions	9
Representation formulas and pointwise properties for Barron functions	9
Index estimates for surfaces with constant mean curvature in 3-dimensional manifolds	9
New weighted sharp Trudinger–Moser inequalities defined on the whole euclidean space $$ {\mathbb {R}}^N $$ and applications	9
Energy scattering for radial focusing inhomogeneous bi-harmonic Schrödinger equations	9
The antiferromagnetic XY model on the triangular lattice: chirality transitions at the surface scaling	9
A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers	9
Hessian estimates for Lagrangian mean curvature equation	8
Convergence rate of general entropic optimal transport costs	8
Pseudoconvexity for the special Lagrangian potential equation	8
Uniqueness of the critical point for semi-stable solutions in $$\mathbb {R}^2$$	8
Nonlocal Harnack inequalities in the Heisenberg group	8
Travelling helices and the vortex filament conjecture in the incompressible Euler equations	8
The effects of diffusion on the dynamics of a Lotka-Volterra predator-prey model with a protection zone	8
A combinatorial Yamabe problem on two and three dimensional manifolds	8
Nonlocal semilinear elliptic problems with singular nonlinearity	8
Flux & radii within the subconformal capacity	8
Bourgain–Brezis–Mironescu–Maz’ya–Shaposhnikova limit formulae for fractional Sobolev spaces via interpolation and extrapolation	8
A type of Brézis–Oswald problem to $$\Phi $$-Laplacian operator with strongly-singular and gradient terms	8
Optimal incompatible Korn–Maxwell–Sobolev inequalities in all dimensions	8
Existence and asymptotic behavior of normalized ground states for Sobolev critical Schrödinger systems	8
Eigenvalues of the Laplacian with moving mixed boundary conditions: the case of disappearing Dirichlet region	7
Asymptotic expansions for singular solutions of $$\Delta u+e^u=0$$ in a punctured disc	7
Uniform a priori estimates for solutions of higher critical order fractional equations	7
Almost minimizers for the thin obstacle problem	7
Non-uniqueness in law for the Boussinesq system forced by random noise	7
The generalized porous medium equation on graphs: existence and uniqueness of solutions with $$\ell ^1$$ data	7
Nonrelativistic limit and some properties of solutions for nonlinear Dirac equations	7
Linear stability estimates for Serrin’s problem via a modified implicit function theorem	7
Global solvability in a Keller-Segel-growth system with indirect signal production	7
Ground states of elliptic problems over cones	7
Inverse mean curvature evolution of entire graphs	7
Bourgain–Brezis–Mironescu convergence via Triebel-Lizorkin spaces	7
On renormalized solutions to elliptic inclusions with nonstandard growth	7
Local uniqueness of ground states for rotating bose-einstein condensates with attractive interactions	7
Small order asymptotics for nonlinear fractional problems	7
A fractional Hadamard formula and applications	7
Long time behavior for a periodic Lotka–Volterra reaction–diffusion system with strong competition	7
Solutions to Hamilton–Jacobi equation on a Wasserstein space	7
G-invariant Szegő kernel asymptotics and CR reduction	7
Augmented Lagrangian methods for degenerate Hamilton–Jacobi equations	7
Stable determination by a single measurement, scattering bound and regularity of transmission eigenfunctions	7
Large conformal metrics with prescribed Gaussian and geodesic curvatures	7
On elliptic operators with Steklov condition perturbed by Dirichlet condition on a small part of boundary	7
Uniqueness and positivity issues in a quasilinear indefinite problem	7
Existence and nonexistence in the liquid drop model	7
Normalized solutions for Schrödinger equations with mixed dispersion and critical exponential growth in $${\mathbb {R}}^2$$	7
Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas	7
Existence and non-existence of ground states of bi-harmonic equations involving constant and degenerate Rabinowitz potentials	7
Effects of corners in surface superconductivity	7
Derivation of Darcy’s law in randomly perforated domains	7
Sign-changing solutions for a modified nonlinear Schrödinger equation in $${\mathbb {R}}^N$$	7
The Lamm–Rivière system I: $$L^p$$ regularity theory	6
Normalized multi-bump solutions of nonlinear Schrödinger equations via variational approach	6
Stability of radially symmetric, monotone vorticities of 2D Euler equations	6
Saturn ring defect around a spherical particle immersed in a nematic liquid crystal	6
Existence and uniqueness of bounded stable solutions to the Peierls–Nabarro model for curved dislocations	6
Stabilizing effect of magnetic field on the 2D ideal magnetohydrodynamic flow with mixed partial damping	6
Improved regularity for the parabolic normalized p-Laplace equation	6
Natural second-order regularity for parabolic systems with operators having $$(p,\delta )$$-structure and depending only on the symmetric gradient	6
Monotonicity of positive solutions to quasilinear elliptic equations in half-spaces with a changing-sign nonlinearity	6
Density of Lipschitz functions in energy	6
Stability of smooth multi-solitons for the Camassa–Holm equation	6
Geometry of log-concave functions: the $$L_p$$ Asplund sum and the $$L_{p}$$ Minkowski problem	6
Local Lipschitz bounds for solutions to certain singular elliptic equations involving the one-Laplacian	6
On critical Kirchhoff problems driven by the fractional Laplacian	6
Interior Hessian estimates for a class of Hessian type equations	6
Gradient estimates for singular parabolic p-Laplace type equations with measure data	6
Density and positive mass theorems for incomplete manifolds	6
On the constancy theorem for anisotropic energies through differential inclusions	6
Boundedness of solutions to Dirichlet, Neumann and Robin problems for elliptic equations in Orlicz spaces	6
Global existence of smooth solution to relativistic membrane equation with large data	6
Sobolev estimates for fractional parabolic equations with space-time non-local operators	6
Scattering for the non-radial inhomogenous biharmonic NLS equation	6
The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge–Ampère measures	6
An exterior overdetermined problem for Finsler N-Laplacian in convex cones	6
Lifespan estimates for semilinear wave equations with space dependent damping and potential	6
Mixed local and nonlocal equations with measure data	6

Boundary value problems for a special Helfrich functional for surfaces of revolution: existence and asymptotic behaviour	5
A multi-material transport problem with arbitrary marginals	5
The Schrödinger problem on the non-commutative Fisher-Rao space	5
A restricted nonlocal operator bridging together the Laplacian and the fractional Laplacian	5
To what extent is cross-diffusion controllable in a two-dimensional chemotaxis-(Navier–)Stokes system modeling coral fertilization	5
Integral representation and $$\Gamma $$-convergence for free-discontinuity problems with $$p(\cdot )$$-growth	5
From radial symmetry to fractal behavior of aggregation equilibria for repulsive–attractive potentials	5
The fractional $$p\,$$-biharmonic systems: optimal Poincaré constants, unique continuation and inverse problems	5
Hardy–Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs	5
Prescribed mass standing waves for energy critical Hartree equations	5
Absence of positive eigenvalues of magnetic Schrödinger operators	5
Some non-linear systems of PDEs related to inverse problems in conductivity	5
On the cauchy problem of 3D compressible, viscous, heat-conductive navier-stokes-Poisson equations subject to large and non-flat doping profile	5
Superharmonicity of curvature function for the convex level sets of harmonic functions	5
Strong convergence of the Bopp–Podolsky–Schrödinger–Proca system to the Schrödinger–Poisson–Proca system in the electro-magneto-static case	5
$${\mathscr {A}}$$-quasiconvexity and partial regularity	5
On center of mass and foliations by constant spacetime mean curvature surfaces for isolated systems in General Relativity	5
The global curvature estimate for the $$n-2$$ Hessian equation	5
Müller–Zhang truncation for general linear constraints with first or second order potential	5
The Dirichlet-to-Neumann operator associated with the 1-Laplacian and evolution problems	5
Setting the Free Material Design problem through the methods of optimal mass distribution	5
A non-local quasi-linear ground state representation and criticality theory	5
Boundary layer problems for the two-dimensional inhomogeneous incompressible magnetohydrodynamics equations	5
Deformation of framed curves with boundary conditions	5
Wolff potentials and measure data vectorial problems with Orlicz growth	5
Infinitely many positive solutions of nonlinear Schrödinger equations	5
Generalized Brezis–Seeger–Van Schaftingen–Yung formulae and their applications in ball Banach Sobolev spaces	5
Low entropy and the mean curvature flow with surgery	5
Boundedness of non-local operators with spatially dependent coefficients and $$L_p$$-estimates for non-local equations	5
On the second boundary value problem for Lagrangian mean curvature equation	5
Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids	5
Riesz transforms of a general Ornstein–Uhlenbeck semigroup	5
A Talenti-type comparison theorem for $${{\,\mathrm{RCD}\,}}(K,N)$$ spaces and applications	5
Convex hypersurfaces with prescribed scalar curvature and asymptotic boundary in hyperbolic space	5
Collapsing of the line bundle mean curvature flow on Kähler surfaces	5
The Nirenberg problem on high dimensional half spheres: the effect of pinching conditions	5
Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group	5
The Euler–Helfrich functional	5
Uniqueness and characterization of local minimizers for the interaction energy with mildly repulsive potentials	5
Upper and lower bounds for the Dunkl heat kernel	5
Quantitative symmetry in a mixed Serrin-type problem for a constrained torsional rigidity	5
Sharp conditions for the linearization of finite elasticity	5
On torsional rigidity and ground-state energy of compact quantum graphs	5
On a sharp inequality of Adimurthi–Druet type and extremal functions	4
Spectral invariants of the perturbed polyharmonic Steklov problem	4
Stability and bifurcation in a reaction–diffusion–advection predator–prey model	4
Radial single point rupture solutions for a general MEMS model	4
Sharp Rellich–Leray inequality with any radial power weight for solenoidal fields	4
Linear inverse problems with Hessian–Schatten total variation	4
Perturbed Schrödinger lattice systems with superlinear terms: Multiplicity of homoclinic solutions	4
On n-superharmonic functions and some geometric applications	4
Classification of solutions for some elliptic system	4
Well-posedness of the free boundary problem in incompressible MHD with surface tension	4
Gradient estimates for divergence form parabolic systems from composite materials	4
Energy asymptotics in the three-dimensional Brezis–Nirenberg problem	4
Global Existence, Regularity and Boundedness in a Higher-dimensional Chemotaxis-Navier-Stokes System with Nonlinear Diffusion and General Sensitivity	4
Conservation laws for even order systems of polyharmonic map type	4
Complete $$\lambda $$-surfaces in $${\mathbb {R}}^3$$	4
Compactness and existence results of the prescribing fractional Q-curvature problem on $$\mathbb {S}^n$$	4
An isoperimetric problem with a competing nonlocal singular term	4
Local pointwise second derivative estimates for strong solutions to the $$\sigma _k$$-Yamabe equation on Euclidean domains	4
Global classical solutions of 3D compressible viscoelastic system near equilibrium	4
Global regularity for degenerate/singular parabolic equations involving measure data	4
Inequalities between torsional rigidity and principal eigenvalue of the p-Laplacian	4
Global transversal stability of Euclidean planes under skew mean curvature flow evolutions	4
Standing wave solutions of Maxwell–Dirac systems	4
Homogenization of the two-dimensional evolutionary compressible Navier–Stokes equations	4
Uniform estimates for Stokes equations in a domain with a small hole and applications in homogenization problems	4
On the heat content functional and its critical domains	4
Layer potentials for Lamé systems and homogenization of perforated elastic medium with clamped holes	4
Mixed boundary valued problems for linear and nonlinear wave equations in domains with fractal boundaries	4
Large solutions to quasilinear problems involving the p-Laplacian as p diverges	4
On subhomogeneous indefinite p-Laplace equations in the supercritical spectral interval	4
Hölder regularity for parabolic fractional p-Laplacian	4
Incompressible impinging jet flow with gravity	4
Upper bounds for the Steklov eigenvalues on trees	4
Harnack’s estimate for a mixed local–nonlocal doubly nonlinear parabolic equation	4
An optimal pinching theorem of minimal Legendrian submanifolds in the unit sphere	4
Bounded solutions for quasilinear modified Schrödinger equations	4
Many-particle limit for a system of interaction equations driven by Newtonian potentials	4
Optimal transport of vector measures	4
A Rigidity Theorem for the deformed Hermitian-Yang-Mills equation	4
Global nonlinear stability of one kind of large solutions to evolutionary Faddeev model	4
Nonlinear nonlocal Douglas identity	4
Caffarelli–Kohn–Nirenberg inequalities for curl-free vector fields and second order derivatives	4
Heterogeneous gradient flows in the topology of fibered optimal transport	4
Non-homogeneous Dirichlet-transmission problems for the anisotropic Stokes and Navier-Stokes systems in Lipschitz domains with transversal interfaces	4
Multiple high energy solutions for fractional Schrödinger equation with critical growth	4
One-dimensionality of the minimizers in the large volume limit for a diffuse interface attractive/repulsive model in general dimension	4
Optimal measure transportation with respect to non-traditional costs	4
Bubble towers in the ancient solution of energy-critical heat equation	4
Generic existence of multiplicity-1 minmax minimal hypersurfaces via Allen–Cahn	4
The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces	4
Continuous solutions to Monge–Ampère equations on Hermitian manifolds for measures dominated by capacity	4
The existence of embedded G-invariant minimal hypersurface	4