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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

Corresponding Author:[email protected]

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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.
27 Apr 2020Submitted to Mathematical Methods in the Applied Sciences
01 May 2020Submission Checks Completed
01 May 2020Assigned to Editor
05 May 2020Reviewer(s) Assigned
21 Sep 2020Review(s) Completed, Editorial Evaluation Pending
23 Dec 2020Editorial Decision: Revise Major
25 Dec 20201st Revision Received
25 Dec 2020Submission Checks Completed
25 Dec 2020Assigned to Editor
29 Sep 2021Review(s) Completed, Editorial Evaluation Pending
29 Sep 2021Editorial Decision: Accept