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ON THE EXISTENCE OF EXTREMALS FOR THE SOBOLEV TRACE EMBEDDING THEOREM WITH CRITICAL EXPONENT

Published online by Cambridge University Press:  08 February 2005

JULIÁN FERNÁNDEZ BONDER  and
JULIO D. ROSSI
JULIÁN FERNÁNDEZ BONDER
Affiliation:
Departemento de Matemática, FCEyN, UBA (1428) Buenos Aires, Argentinajfbonder@dm.uba.ar
JULIO D. ROSSI
Affiliation:
Departamento de Matemática, Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chilejrossi@riemann.mat.puc.cl
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Abstract

In this paper, the existence problem is studied for extremals of the Sobolev trace inequality $W^{1,p}(\Omega)\to L^{p_*}(\partial\Omega)$, where $\Omega$ is a bounded smooth domain in $\RR^N$, $p_*=p(N-1)/(N-p)$ is the critical Sobolev exponent, and $1<p<N$.

Keywords

35J65 (primary)35B33 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 1 , January 2005 , pp. 119 - 125
Copyright
© The London Mathematical Society 2005

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Footnotes

Supported by Fundacion Antorchas, CONICET, ANPCyT PICT Nos 05009 and 10608, and UBA X066.