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Annales Henri Poincaré

, Volume 16, Issue 6, pp 1489–1508 | Cite as

Sharp Embedding of Sobolev Spaces Involving General Kernels and its Application

  • Huyuan Chen
  • Hichem HajaiejEmail author
Article
  • 195 Downloads

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 the embedding. 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.

Keywords

Weak Solution Sobolev Space Homogeneous Dirichlet Boundary Condition Mountain Pass Theorem General Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsJiangxi Normal UniversityJiangxiPeople’s Republic of China
  2. 2.Department of Mathematics, College of ScienceKing Saud UniversityRiyadhSaudi Arabia

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