Weighted Hardy-Sobolev inequality and global existence result of thermoelastic system on manifolds with corner-edge singularities
• Morteza Koozehgar Kalleji
Morteza Koozehgar Kalleji
Arak University
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## Abstract

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$\acute{e}$ 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.

#### Peer review status:UNDER REVIEW

27 Apr 2020Submitted to Mathematical Methods in the Applied Sciences
01 May 2020Assigned to Editor
01 May 2020Submission Checks Completed
05 May 2020Reviewer(s) Assigned
21 Sep 2020Review(s) Completed, Editorial Evaluation Pending