Brahim Bougherara, Jacques Giacomoni, Jesus Hernandez
In this article we study the semilinear singular elliptic problem
where is a regular bounded domain of , , which behaves as as with the distance function up to the boundary and . We discuss the existence, uniqueness and stability of the weak solution. We also prove accurate estimates on the gradient of the solution near the boundary. Consequently, we can prove that the solution belongs to for which is optimal if .
Published November 20, 2015.
Math Subject Classifications: 35B65.
Key Words: Semilinear elliptic and singular problems; comparison principle; regularity of the gradient of solutions; Hardy inequalities.
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| Brahim Bougherara |
Département de mathématiques
ENS de Kouba
| Jacques Giacomoni |
LMAP (UMR CNRS 5142) Bat. IPRA
Avenue de l'Université F-64013 Pau, France
| Jesus Hernández |
Departemento de Matemáticas
Universidad Autónoma de Madrid
28049 Madrid, Spain
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