A mass transportation approach for Sobolev inequalities in variable exponent spaces

Abstract

In this paper we provide a proof of the Sobolev-Poincar´e inequality for variable exponent spaces by means of mass transportation methods, in the spirit of [4]. The importance of this approach is that the method is flexible enough to deal with different inequalities. As an application, we also deduce the Sobolev-trace inequality improving the result of [11] by obtaining an explicit dependence of the exponent in the constant.