On the existence of an extremal function in critical Sobolev trace embedding theorem

DOI10.1016/j.jfa.2010.02.018zbMath1201.46033OpenAlexW2038790690MaRDI QIDQ971841

A. B. Reznikov, Alexander I. Nazarov

Publication date: 17 May 2010

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2010.02.018

zbMATH Keywords

sharp constantscritical trace Sobolev inequalitycritical trace Sobolev-Poincaré inequality

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (6)

Multiplicity of positive solutions for a critical quasilinear Neumann problem ⋮ Lyapunov inequality for an elliptic problem with the Robin boundary condition ⋮ On the Sobolev trace theorem for variable exponent spaces in the critical range ⋮ On the Hénon equation with a Neumann boundary condition: asymptotic profile of ground states ⋮ The role of the mean curvature in a Hardy-Sobolev trace inequality ⋮ SHARP CONSTANTS IN THE POINCARÉ, STEKLOV AND RELATED INEQUALITIES (A SURVEY)

Cites Work

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• Best constant in Sobolev trace inequalities on the half-space
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Optimal Sobolev inequalities of arbitrary order on compact Riemannian manifolds
• Dirichlet and Neumann problems to critical Emden-Fowler type equations
• ON THE EXISTENCE OF EXTREMALS FOR THE SOBOLEV TRACE EMBEDDING THEOREM WITH CRITICAL EXPONENT
• The pseudo-p-Laplace eigenvalue problem and viscosity solutions asp→ ∞

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