Sharp embedding of Sobolev spaces involving general kernels and its application

Huyuan Chen, Hichem Hajaiej

Published 2013-11-27, updated 2014-04-04Version 2

The purpose of this paper is to extend the embedding theorem of Sobolev spaces involving general kernels and we provide a sharp critical exponent in these embeddings. As an application, solutions for equations driven by a general integro-differential operator, with homogeneous Dirichlet boundary conditions, is established by using the Mountain Pass Theorem.