Cone Sobolev inequality and Dirichlet problem for nonlinear elliptic equations on a manifold with conical singularities

• DOI: 10.1007/s00526-011-0418-7
• Publication Date: 2011-03-29T08:26:32Z
• Authors: Hua Chen; Xiaochun Liu; Yawei Wei
• Keywords: Sobolev inequality; Manifold (fluid mechanics); Cone (formal languages)

In present work, we first establish the corresponding Sobolev inequality and Poincare inequality on the cone Sobolev spaces, and then, as an application of such inequalities, we prove the existence of non-trivial weak solution for Dirichlet boundary value problem for a class of non-linear elliptic equation on manifolds with conical singularities.