On the Sobolev embedding theorem for variable exponent spaces in the critical range

Details On the Sobolev embedding theorem for variable exponent spaces in the critical range On the Sobolev embedding theorem for variable exponent spaces in the critical range

2011-11-29

arxiv.org/abs/1111.6952v1

Mathematics

Analysis of PDEs

15 pages, submitted

Scientific paper

In this paper we study the Sobolev embedding theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. The proof is based on a suitable refinement of the estimates in the Concentration--Compactness Theorem for variable exponents and an adaptation of a convexity argument due to P.L. Lions, F. Pacella and M. Tricarico.

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