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Sharp estimates of solution of an elliptic problem on a family of open non-convex planar sectors
  • Abdelkader Tami,
  • Abdelaziz Douah,
  • Mounir Tlemcani
Abdelkader Tami
University of Science and Technology of Oran - Mohamed Boudiaf - USTO-MB

Corresponding Author:abdelkader.tami@univ-usto.dz

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Abdelaziz Douah
University of Science and Technology of Oran - Mohamed Boudiaf - USTO-MB
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Mounir Tlemcani
University of Science and Technology of Oran - Mohamed Boudiaf - USTO-MB
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Abstract

Based on partial Fourier series analysis, we adapt on a model case a new approach to classical results obtained in the literature describing the singularities of a family a solutions of a second order elliptic problems on open non-convex planar sectors. The method allows the exhibition of singular and regular frequencies, explicit decomposition and description of coefficients of singularities of the solution. As a main result, explicit and sharp estimates with respect to the opening angle parameter are obtained via this method. They are not uniform near π where corners have opening angle generating a jump of singularity in Sobolev exponent, contrarily to the results obtained in A. Tami (2016),(2019),(2021) for harmonic and/or biharmonic problems on a family of convex planar sectors.
10 Mar 2024Submitted to Mathematical Methods in the Applied Sciences
29 Mar 2024Reviewer(s) Assigned
09 Jul 2024Review(s) Completed, Editorial Evaluation Pending
10 Jul 2024Editorial Decision: Revise Major
18 Jul 20241st Revision Received
19 Jul 2024Assigned to Editor
19 Jul 2024Submission Checks Completed
19 Jul 2024Review(s) Completed, Editorial Evaluation Pending
21 Jul 2024Reviewer(s) Assigned
13 Aug 2024Editorial Decision: Accept