Symmetry results for functions yielding best constants in Sobolev-type inequalities

Bernhard Kawohl

doi:10.3934/dcds.2000.6.683

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2000, Volume 6, Issue 3: 683-690. Doi: 10.3934/dcds.2000.6.683

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Symmetry results for functions yielding best constants in Sobolev-type inequalities

Bernhard Kawohl^1,

1.
Mathematisches Institut, Universität zu Köln, D - 50923 Köln

Received: October 31, 1999

Revised: February 29, 2000

Published: June 2000

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Abstract

I report on symmetry results for functions which yield sharp constants in various Sobolev-type inequalities. One of these results relies on a surprising convexity property.

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Mathematics Subject Classification: 49R05, 35J20, 35J65, 35B35.

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