Nonlinear weighted elliptic equations with L 1 data
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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 of a weak solution of elliptic problem (P) defined by
(P)
(
−div(S(x)|∇u|
p−2∇u) + e(x)|u|
p−2u = f in Ω;
u = 0 on ∂Ω,
with f ∈ L
1
(Ω). The weighted p-Laplacian operator Au = −div(S(x)|∇u|
p−2∇u), 1 <
p < ∞ is a pseudo-monotone operator on W
1,p
0
(Ω) despite being well-defined between
W
1,p
0
(Ω) and its dual W−1,p0
(Ω). The method of solving our problem consist of obtaining
local estimates for suitable approximate problems and then passing to the limit.
Description
Keywords
Weighted Sobolev spaces, pseudo-monotone, operator nonlinear, elliptic equation, weak solution