A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces

JULIAN FERNANDEZ BONDER; NICOLAS SAINTIER; ANALIA SILVA

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2016

0022-247X

In this paper, we study the critical Sobolev embeddings W1,p(x)(Ω) ⊂ Lp∗(x)(Ω) forvariable exponent Sobolev spaces from the point of view of the Γ-convergence. More preciselywe determine the Γ-limit of subcritical approximation of the best constant associated with thisembedding. As an application we provide a sufficient condition for the existence of extremalsfor the best constant.