Weighted Hardy–Sobolev inequality and global existence result of thermoelastic system on manifolds with corner‐edge singularities

摘要

This article concerns with the thermoelastic corner‐edge‐type system with singular potential function on a wedge manifold with corner singularities. First, we introduce weighted p‐Sobolev spaces on manifolds with corner‐edge singularities. Then, we prove the corner‐edge‐type Sobolev inequality, Poincar é inequality and Hardy inequality and obtain some results about the compactness of embedding maps on the weighted corner‐edge Sobolev spaces. Finally, as an application of these results, we apply the potential well theory and the Faedo–Galerkin approximations to obtain the global weak solutions for the thermoelastic corner‐edge‐type system 1.1.