☆ 4.4 Article

On the Sobolev trace Theorem for variable exponent spaces in the critical range

ANNALI DI MATEMATICA PURA ED APPLICATA (2014)

Journal

ANNALI DI MATEMATICA PURA ED APPLICATA

Volume 193, Issue 6, Pages 1607-1628

Publisher

SPRINGER HEIDELBERG

DOI: 10.1007/s10231-013-0346-6

Keywords

Sobolev embedding; Variable exponents; Critical exponents; Concentration compactness

Categories

Mathematics, Applied Mathematics

Funding

Universidad de Buenos Aires [UBACYT 20020100100400]
CONICET (Argentina) [PIP 5478/1438]

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Abstract

In this paper, we study the Sobolev trace Theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. Then, we give local conditions on the exponents and on the domain (in the spirit of Adimurthy and Yadava) in order to satisfy such conditions and therefore to ensure the existence of extremals.

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