A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics
From MaRDI portal
Publication:699801
DOI10.1007/s002050200201zbMath1010.35041OpenAlexW1995659973MaRDI QIDQ699801
Marino Badiale, Grabriella Tarantello
Publication date: 25 September 2002
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s002050200201
Partial differential inequalities and systems of partial differential inequalities (35R45) Nonlinear elliptic equations (35J60) Galactic and stellar dynamics (85A05) Euler-Poisson-Darboux equations (35Q05)
Related Items
Qualitative study in a parabolic equation with nonstandard growth conditions and singular medium void ⋮ Critical nonlinear elliptic equations with singularities and cylindrical symmetry. ⋮ Symmetry of positive solutions of fractional Laplacian equation and system with Hardy-Sobolev exponent on the unit ball ⋮ In between the inequalities of Sobolev and Hardy ⋮ Weighted Caffarelli-Kohn-Nirenberg type inequality on the Heisenberg group ⋮ Weighted fractional Sobolev inequality in \(\mathbb R^N\) ⋮ Existence and multiplicity results for an elliptic problem involving cylindrical weights and a homogeneous term \(\mu \) ⋮ Hardy-Sobolev extremals, hyperbolic symmetry and scalar curvature equations ⋮ Hardy-Sobolev inequality with singularity a curve ⋮ Hardy-type inequalities derived from \(p\)-harmonic problems ⋮ Existence and non-existence of solutions to elliptic equations related to the Caffarelli-Kohn-Nirenberg inequalities ⋮ Hardy-Sobolev inequalities in half-space and some semilinear elliptic equations with singular coefficients ⋮ Existence and multiplicity results for a weighted \(p\)-Laplace equation involving Hardy potentials and critical nonlinearities ⋮ Global weighted regularity for the 3D axisymmetric MHD equations ⋮ Critical singular problems via concentration-compactness lemma ⋮ Generalized linking-type theorem with applications to strongly indefinite problems with sign-changing nonlinearities ⋮ Horizontal weighted Hardy-Rellich type inequalities on stratified Lie groups ⋮ Global existence and blow-up of solutions to a singular non-Newton polytropic filtration equation with critical and supercritical initial energy ⋮ Construction of solutions for a critical Grushin problem with competing potentials ⋮ Best constants in the Hardy-Rellich inequalities and related improvements ⋮ Multiple solutions to nonlinear Schrödinger equations with singular electromagnetic potential ⋮ Cylindrical solutions and ground state solutions to weighted Kirchhoff equations ⋮ Infinitely many solutions for a Hardy-Sobolev equation involving critical growth ⋮ Qualitative properties of positive solutions of quasilinear equations with Hardy terms ⋮ Multiple positive solutions for a nonlinear elliptic equation involving Hardy-Sobolev-Maz'ya term ⋮ Global existence and blow up of solutions for pseudo-parabolic equation with singular potential ⋮ Improved Sobolev inequalities and critical problems ⋮ Global existence, extinction, and non-extinction of solutions to a fast diffusion \(p\)-Laplace evolution equation with singular potential ⋮ Weighted Caffarelli-Kohn-Nirenberg type inequalities related to Grushin type operators ⋮ Global smooth axisymmetric solutions of 3-D inhomogeneous incompressible Navier-Stokes system ⋮ On \(G\)-symmetric solutions of critical elliptic equations of Caffarelli-Kohn-Nirenberg type ⋮ Caffarelli-Kohn-Nirenberg and Sobolev type inequalities on stratified Lie groups ⋮ Geometric Hardy's inequalities with general distance functions ⋮ Long-time asymptotics of axisymmetric Navier-Stokes equations in critical spaces ⋮ Initial boundary value problem for \(p\)-Laplacian type parabolic equation with singular potential and logarithmic nonlinearity ⋮ Infinitely many solutions for a critical Grushin-type problem via local Pohozaev identities ⋮ On first order interpolation inequalities with weights on the Heisenberg group ⋮ On first order interpolation inequalities with weights on the H-type group ⋮ Remarks on a Hardy-Sobolev inequality. ⋮ Weighted polyharmonic equation with Navier boundary conditions in a half space ⋮ Global existence and blow-up of solutions to a class of nonlocal parabolic equations ⋮ Multiple solutions to \(p\)-Laplacian equation with singularity and cylindrical symmetry. ⋮ Anisotropic Caffarelli-Kohn-Nirenberg type inequalities ⋮ A note about a Caffarelli-Kohn-Nirenberg type inequality for Euclidean submanifolds ⋮ A global compactness result with applications to a nonlinear elliptic equation arising in astrophysics ⋮ Symmetry and regularity of extremals of an integral equation related to the Hardy-Sobolev inequality ⋮ Ground state solutions of a critical problem involving cylindrical weights ⋮ Extremals for fractional order Hardy-Sobolev-Maz'ya inequality ⋮ On nonhomogeneous singular elliptic equations with cylindrical weights ⋮ Asymptotic behavior for elliptic problems with singular coefficient and nearly critical Sobolev growth ⋮ A class of Caffarelli-Kohn-Nirenberg type inequalities on the \(H\)-type group ⋮ Extremals for Hardy-Sobolev type inequalities with monomial weights ⋮ On weighted regularity criteria for the axisymmetric Navier-Stokes equations ⋮ Nontrivial solutions for a class of critical elliptic equations of Caffarelli-Kohn-Nirenberg type ⋮ Weighted \(L^p\)-Hardy and \(L^p\)-Rellich inequalities with boundary terms on stratified Lie groups ⋮ On existence of mimimizers for the Hardy-Sobolev-Maz'ya inequality ⋮ Global existence and extinction of solutions to a fast diffusion \(p\)-Laplace equation with special medium void ⋮ Admissible function spaces for weighted Sobolev inequalities ⋮ A nonlinear elliptic equation with singular potential and applications to nonlinear field equations ⋮ A new blow-up condition for a parabolic equation with singular potential ⋮ Singular elliptic problems in \(\mathbb R^N\) with critical Sobolev-Hardy exponents ⋮ On weighted logarithmic-Sobolev \& logarithmic-Hardy inequalities ⋮ Existence and multiplicity of solutions for a supercritical elliptic problem in unbounded cylinders ⋮ Regularity of 3D axisymmetric Navier-Stokes equations ⋮ A Liouville type theorem for higher order Hardy-Hénon equation in \(\mathbb R^n\) ⋮ Qualitative properties of solutions for an integral system related to the Hardy-Sobolev inequality ⋮ Global existence and blow-up of solutions for a non-Newton polytropic filtration system with special volumetric moisture content ⋮ Positive solutions to a semilinear elliptic equation with a Sobolev-Hardy term ⋮ Classification of solutions of a critical Hardy--Sobolev operator ⋮ Sign-changing solutions to elliptic problems with two critical Sobolev-Hardy exponents ⋮ Existence of extremal functions for a Hardy-Sobolev inequality ⋮ Cylindrical symmetry of extremals of a Hardy-Sobolev inequality ⋮ Hardy and Rellich inequalities for submanifolds in Hadamard spaces ⋮ A logarithmic Hardy inequality ⋮ Hardy-Sobolev inequalities and hyperbolic symmetry ⋮ On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and \(p\)-sub-Laplacian inequalities on stratified groups ⋮ Global existence and blow-up of solutions to a semilinear heat equation with singular potential and logarithmic nonlinearity ⋮ Factorizations and Hardy-Rellich inequalities on stratified groups ⋮ Generalised nonlinear Picone identities for \(p\)-sub-Laplacians and \(p\)-biharmonic operators and applications ⋮ Optimal Hardy-Sobolev inequalities on compact Riemannian manifolds ⋮ Positive solutions for the Hardy-Sobolev-Maz'ya equation with Neumann boundary condition ⋮ On a Sobolev-type inequality related to the weighted \(p\)-Laplace operator ⋮ The compactness and the concentration compactness via \(P\)-capacity ⋮ $L^{p}$ estimates and asymptotic behavior for finite energy solutions of extremals to Hardy-Sobolev inequalities ⋮ Existence of extremals for the Maz'ya and for the Caffarelli-Kohn-Nirenberg inequalities ⋮ A Caffarelli–Kohn–Nirenberg-type inequality with variable exponent and applications to PDEs ⋮ Elliptic equations with critical growth and a large set of boundary singularities ⋮ Apriori decay estimates for Hardy-Sobolev-Maz'ya equations ⋮ Infinitely many sign-changing solutions for the Hardy-Sobolev-Maz'ya equation involving critical growth ⋮ Hardy-Sobolev inequality with higher dimensional singularity ⋮ Caccioppoli-type estimates and Hardy-type inequalities derived from weighted \(p\)-harmonic problems ⋮ A note about the generalized Hardy-Sobolev inequality with potential in \(L^{p,d}(\mathbb R^n)\) ⋮ Hardy-Sobolev type inequalities on the H-type group ⋮ A survey of Hardy type inequalities on homogeneous groups ⋮ A multi-dimension blow-up problem to a porous medium diffusion equation with special medium void ⋮ On the generalised Brézis-Nirenberg problem ⋮ On a fractional Hardy-Sobolev inequality with two-variables ⋮ A global compactness result with applications to a Hardy-Sobolev critical elliptic system involving coupled perturbation terms ⋮ On a strongly damped semilinear wave equation with time-varying source and singular dissipation ⋮ On a singular parabolic \(p\)-biharmonic equation with logarithmic nonlinearity ⋮ Global well-posedness for pseudo-parabolic p-Laplacian equation with singular potential and logarithmic nonlinearity ⋮ Hardy-Sobolev inequalities with distance to the boundary weight functions ⋮ Multiple Solutions to Cylindrically Symmetric Curl-Curl Problems and Related Schrödinger Equations with Singular Potentials ⋮ On integral equations of Matukuma type ⋮ Cylindrical solutions for a critical Grushin-type equation via local Pohozaev identities ⋮ Local regularity for nonlinear elliptic and parabolic equations with anisotropic weights ⋮ Regularity criteria of the axisymmetric Navier-Stokes equations and Hardy-Sobolev inequality in mixed Lorentz spaces ⋮ Hardy and Hardy–Rellich type inequalities with Bessel pairs ⋮ Unnamed Item ⋮ INFINITELY MANY SOLUTIONS FOR HARDY–SOBOLEV–MAZ'YA EQUATION INVOLVING CRITICAL GROWTH ⋮ On the best constant in a Hardy–Sobolev inequality ⋮ An anisotropic Sobolev–Hardy inequality with application to 3D axisymmetric Navier–Stokes equations ⋮ Liouville-type theorems and existence results for stable solutions to weighted Lane–Emden equations ⋮ Unnamed Item ⋮ Convergence of Parareal Algorithms for PDEs with Fractional Laplacian and a Non-Constant Coefficient ⋮ Influence of an L^{p}-perturbation on Hardy-Sobolev inequality with singularity a curve ⋮ Cylindrical Hardy type inequalities with Bessel pairs
