Brahim Bougherara, Jacques Giacomoni, Jesus Hernandez
Abstract:
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 16308--Alger, Algérie email: brahim.bougherara@univ-pau.fr | |
Jacques Giacomoni LMAP (UMR CNRS 5142) Bat. IPRA Avenue de l'Université F-64013 Pau, France email: jacques.giacomoni@univ-pau.fr | |
Jesus Hernández Departemento de Matemáticas Universidad Autónoma de Madrid 28049 Madrid, Spain email: jesus.hernandez@uam.es |
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