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

JULIAN FERNANDEZ BONDER; N. SAINTIER; A. SILVA

JOURNAL OF DIFFERENTIAL EQUATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2012 p. 1604 - 1620

0022-0396

In this paper we study the Sobolev embedding theorem for variable exponent spaces with critical exponents. We nd conditions on the best constant in order to guaranty the existence of extremals. The proof is based on a suitable renement 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.