Asian Journal of Mathematics

Volume 17 (2013)

Number 3

Logarithmic Sobolev trace inequalities

Pages: 569 – 582

DOI: https://dx.doi.org/10.4310/AJM.2013.v17.n3.a8

Authors

Filomena Feo (Dipartimento di Ingegneria, Università degli Studi di Napoli “Pathenope”, Napoli, Italy)

Maria Rosaria Posteraro (Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II, Complesso Universitario Monte S. Angelo, Napoli, Italy)

Abstract

We prove a logarithmic Sobolev trace inequality and we study the trace operator in the weighted Sobolev space $W^{1,p} (\Omega , \gamma)$ for sufficiently regular domain, where $\gamma$ is the Gauss measure. Applications to PDE are also considered.

Keywords

trace inequality, Gauss measure, embedding theorems

2010 Mathematics Subject Classification

46E30, 46E35

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Published 16 October 2013