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Weighted Hardy inequality with higher dimensional singularity on the boundary |
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| Authors: | Mouhamed Moustapha Fall Fethi Mahmoudi |
| Institution: | 1. African Institute for Mathematical Sciences of Senegal, AIMS-Senegal KM 2, Route de Joal, BP: 1418, Mbour, Senegal 2. Departamento de Ingenieria Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile |
| Abstract: | Let \(\Omega \) be a smooth bounded domain in \(\mathbb R ^N\) with \(N\ge 3\) and let \(\Sigma _k\) be a closed smooth submanifold of \(\partial \Omega \) of dimension \(1\le k\le N-2\) . In this paper we study the weighted Hardy inequality with weight function singular on \(\Sigma _k\) . In particular we provide necessary and sufficient conditions for existence of minimizers. |
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