Solvability of a fourth order elliptic problem in a bounded sector, part I
| Autor: | Labbas, Rabah, Maingot, Stéphane, Thorel, Alexandre |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s40574-023-00401-8 |
| Popis: | The purpose of this article (composed of two parts) is the study of the generalized dispersal operator of a reaction-diffusion equation in $L^p$-spaces set in the finite conical domain $S_{\omega,\rho}$ of angle $\omega>0$ and radius $\rho$ > 0 in $\mathbb{R}^2$. This first part is devoted to the behavior of the solution near the top of the cone which is completely described in the weighted Sobolev space $W^{4,p}_{3-\frac{1}{p}}(S_{\omega,\rho_0})$, $\rho_0 \leqslant \rho$, see Theorem 2.2. Comment: Bollettino dell'Unione Matematica Italiana, 2023. arXiv admin note: substantial text overlap with arXiv:2207.05404 |
| Databáze: | arXiv |
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