On the existence of extremal functions in sobolev embedding theorems with critical exponents

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Department of Mathematical Physics

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Cite this

DOI

https://doi.org/10.1090/S1061-0022-06-00929-0
Final published version

A. V. Demyanov
A. I. Nazarov

Sufficient conditions for the existence of extremal functions in Sobolevtype inequalities on manifolds with or without boundary are established. Some of these conditions are shown to be sharp. Similar results for embeddings in some weighted L_q-spaces are obtained.

Original language	English
Pages (from-to)	773-796
Number of pages	24
Journal	St. Petersburg Mathematical Journal
Volume	17
Issue number	5
DOIs	https://doi.org/10.1090/S1061-0022-06-00929-0
State	Published - 1 Jan 2006

Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

Research areas

Critical exponent, Hardy–Sobolev inequality, Minimizers, P-Laplacian, Sobolev inequality, Sobolev–Poincaré inequality

ID: 45872899