Best constants in Sobolev inequalities on manifolds with boundary in the presence of symmetries and applications

DOI10.1016/j.bulsci.2007.04.002zbMath1155.58010OpenAlexW2000385479WikidataQ126265481 ScholiaQ126265481MaRDI QIDQ950540

Nikos Labropoulos, Athanase Cotsiolis

Publication date: 30 October 2008

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2007.04.002

zbMATH Keywords

symmetrymanifold with boundary\(p\)-LaplacianSobolev inequalitybest constantSobolev trace inequalitycritical of supercritical exponent

Mathematics Subject Classification ID

Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (8)

On the best constants in Sobolev inequalities on the solid torus in the limit case \(p = 1\) ⋮ Sharp Nash inequalities on manifolds with boundary in the presence of symmetries ⋮ On a weak solution for a doubly critical fourth-order semilinear elliptic equation in a compact manifold ⋮ Ledoux-type rigidity results on manifolds with boundary in the presence of symmetries ⋮ Existence and multiplicity results for nonlinear critical Neumann problem on compact Riemannian manifolds ⋮ Non-radial solutions of a supercritical equation in expanding domains: the limit case ⋮ Exponential elliptic boundary value problems on a solid torus in the critical of supercritical case ⋮ Vector analysis on symmetric manifolds and Sobolev inequalities

Cites Work

• Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
• Problèmes de Neumann non linéaires sur les variétés riemanniennes
• The concentration-compactness principle in the calculus of variations. The limit case. I
• Problèmes isoperimetriques et espaces de Sobolev
• Sobolev spaces in the presence of symmetries
• Sharp Sobolev inequalities involving boundary terms
• Best constants in Sobolev trace inequalities
• Optimal constants in critical Sobolev inequalities on Riemannian manifolds in the presence of symmetries
• Best constants in Sobolev inequalities on Riemannian manifolds in the presence of symmetries
• Nonlinear elliptic equations with supercritical Sobolev exponent
• On some nonlinear equations involving the \(p\)-Laplacian with critical Sobolev growth
• A strong maximum principle for some quasilinear elliptic equations
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