Abstract
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.
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Labbas, R., Maingot, S. & Thorel, A. Solvability of a fourth order elliptic problem in a bounded sector, part I. Boll Unione Mat Ital (2023). https://doi.org/10.1007/s40574-023-00401-8
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DOI: https://doi.org/10.1007/s40574-023-00401-8