A Stability Result for Extremal Functions for Some Sharp Sobolev Inequalities with Critical Exponent

DOI10.1080/00036810008840851zbMath1026.35037OpenAlexW1973292394WikidataQ58242545 ScholiaQ58242545MaRDI QIDQ2729481

Bruno Nazaret

Publication date: 22 July 2001

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036810008840851

zbMATH Keywords

stabilityvariational methodscritical exponentnonlinear elliptic equation\(p\)-LaplacianSobolev inequalitiesSobolev embeddingbest constant problemsconcentration-compactness theorem

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Stability in context of PDEs (35B35) Nonlinear elliptic equations (35J60) Variational methods for second-order elliptic equations (35J20)

Cites Work

• Local and global properties of solutions of quasilinear elliptic equations
• Regularity for a more general class of quasilinear equations
• Best constant in Sobolev inequality
• Nodal solutions for equations of scalar curvature type on the sphere
• Existence and multiplicity of nodal solutions for nonlinear elliptic equations with critical Sobolev growth
• A strong maximum principle for some quasilinear elliptic equations
• Quasilinear elliptic equations involving critical Sobolev exponents
• Generalized scalar curvature type equations on compact Riemannian manifolds

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