Existence and regularity of the solution of some elliptic problems
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Date
2024
Journal Title
Journal ISSN
Volume Title
Publisher
Mohamed Boudiaf University of M'sila
Abstract
in this work, we prove the existence and regularity of a weak solutions of elliptic problem
(P) defined by
(P)
(
Au = f in Ω;
u = 0 on ∂Ω,
the operator Au = −div(| ∇u |
p−2 ∇u), 1 < p < ∞ is a pseudo-monotone operator,
f ∈ L
1
(Ω). The method of solving our problem consist of obtaining local estimates for
suitable approximate problems and then passing to the limit.
Description
Keywords
Sobolev spaces, pseudo-monotone, operator nonlinear, elliptic equation, weak solution