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


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.


Weak Solution Sobolev Space Homogeneous Dirichlet Boundary Condition Mountain Pass Theorem General Kernel 
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© 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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