Sharp embedding of Sobolev spaces involving general kernels and its application

Abstract

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.

20 pages

References in corpus (3)

• Large solutions to elliptic equations involving fractional Laplacian
• Variational problems related to some fractional kinetic equations
• Weak and strong singular solutions of semilinear fractional elliptic equations