Weak Solutions for elliptic equations with lower-order terms and L 1 data
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Date
2025-06-15
Journal Title
Journal ISSN
Volume Title
Publisher
Mohamed Boudiaf University of M'sila
Abstract
In this work, we study the existence of weak solutions for a class of linear elliptic equations
with lower-order terms and integrable data. More precisely, we consider problems of the
form:
−
u = 0
div(
,
M(x)∇u) + a(x)u = f(x), in
on
Ω
∂
,
Ω,
where Ω ⊂ R
N is a bounded domain, M(x) is an elliptic matrix, a(x) ∈ L
1
(Ω), and
f ∈ L
1
(Ω). Since the right-hand side lies in L
1
(Ω), standard variational methods are not
applicable.
To address this, we construct a sequence of approximate problems whose solutions are
well-defined, and establish uniform a priori estimates. Then, using compactness arguments
and the theory of pseudo-monotone operators, we prove the existence of a weak solution to
the original problem.
Description
Keywords
Elliptic equations, weak solution, integrable data, pseudo-monotone operators, lower-order terms