Cone Sobolev inequality and Dirichlet problem for nonlinear elliptic equations on a manifold with conical singularities
From MaRDI portal
Publication:663332
DOI10.1007/s00526-011-0418-7zbMath1255.58007OpenAlexW2077620214MaRDI QIDQ663332
Hua Chen, Yawei Wei, Xiaochun Liu
Publication date: 14 February 2012
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00526-011-0418-7
Elliptic equations on manifolds, general theory (58J05) Variational methods for second-order elliptic equations (35J20)
Related Items
Multiple solutions for semi-linear corner degenerate elliptic equations with singular potential term ⋮ Global results for semilinear hyperbolic equations with damping term on manifolds with conical singularity ⋮ On decay and blow-up of solutions for a nonlinear Petrovsky system with conical degeneration ⋮ On potential wells to a semilinear hyperbolic equation with damping and conical singularity ⋮ Existence of solutions for degenerate elliptic equations with singular potential on conical singular manifolds ⋮ On the existence with exponential decay and the blow-up of solutions for coupled systems of semi-linear corner-degenerate parabolic equations with singular potentials ⋮ Multiple positive solutions for semi-linear elliptic systems involving sign-changing weight on manifolds with conical singularities ⋮ Global well-posedness for a nonlocal semilinear pseudo-parabolic equation with conical degeneration ⋮ Blow up property for viscoelastic evolution equations on manifolds with conical degeneration ⋮ Existence theorem and global solution for semilinear edge-degenerate hypoelliptic equations ⋮ Lower bounds of Dirichlet eigenvalues for some degenerate elliptic operators ⋮ Global existence, exponential decay and finite time blow-up of solutions for a class of semilinear pseudo-parabolic equations with conical degeneration ⋮ Existence of global solutions for a reaction-diffusion equation with singular coefficients and conical degeneration ⋮ The fractional porous medium equation on manifolds with conical singularities II ⋮ Higher regularity and finite time blow-up to nonlocal pseudo-parabolic equation with conical degeneration ⋮ Existence of solutions for biharmonic equations on conical singular manifolds ⋮ Global existence and nonexistence for semilinear parabolic equations with conical degeneration ⋮ Existence and blow-up of solutions for a class of semilinear pseudo-parabolic equations with cone degenerate viscoelastic term ⋮ Multiple solutions for non-homogeneous degenerate Schrödinger equations in cone Sobolev spaces ⋮ Existence result for a class of semilinear totally characteristic hypoelliptic equations with conical degeneration ⋮ Multiple solutions for semi-linear corner degenerate elliptic equations ⋮ Global existence, finite time blow-up and vacuum isolating phenomena for semilinear parabolic equation with conical degeneration ⋮ Lower and upper bounds of Dirichlet eigenvalues for totally characteristic degenerate elliptic operators ⋮ Asymptotic stability and blow-up of solutions for semi-linear edge-degenerate parabolic equations with singular potentials ⋮ Multiple solutions for a class of nonhomogeneous semilinear equations with critical cone Sobolev exponent ⋮ Biharmonic equations with totally characteristic degeneracy ⋮ Multiplicity and regularity of solutions for infinitely degenerate elliptic equations with a free perturbation ⋮ Invariance and existence analysis for semilinear hyperbolic equations with damping and conical singularity ⋮ Existence of the eigenvalues for the cone degenerate \(p\)-Laplacian ⋮ Semilinear pseudo-parabolic equations on manifolds with conical singularities ⋮ Global existence and non-existence analyses for a semilinear edge degenerate parabolic equation with singular potential term ⋮ Existence theorem for a class of semilinear totally characteristic elliptic equations involving supercritical cone Sobolev exponents ⋮ Global existence and nonexistence for a class of finitely degenerate coupled parabolic systems with high initial energy level ⋮ Generalizations of Troisi's inequality in weighted \(p\)-Sobolev spaces with singularities ⋮ Dirichlet problem for semilinear edge-degenerate elliptic equations with singular potential term ⋮ Global well-posedness for a class of semilinear hyperbolic equations with singular potentials on manifolds with conical singularities ⋮ Multiple positive solutions for degenerate elliptic equations with singularity and critical cone Sobolev exponents ⋮ Multiple solutions for semilinear cone elliptic equations without Ambrosetti-Rabinowitz condition ⋮ The cone Moser–Trudinger inequalities and applications ⋮ Multiple solutions for nonlinear cone degenerate elliptic equations ⋮ Positive solutions for asymptotically linear cone-degenerate elliptic equations
Cites Work
- Unnamed Item
- Unnamed Item
- Existence theorem for a class of semilinear totally characteristic elliptic equations with critical cone Sobolev exponents
- Realizations of differential operators on conic manifolds with boundary
- Semi-linear sub-elliptic equations on the Heisenberg group with a singular potential
- Dual variational methods in critical point theory and applications
- Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
- On the Existence of Positive Solutions of Semilinear Elliptic Equations
- Ellipticity and invertibility in the cone algebra on \(L_p\)-Sobolev spaces