DOI: 10.68381/jca03024 ISSN: 0944-6532
Summability of the Solutions of Nonlinear Elliptic Equations with Right Hand Side Measures
Lucio Boccardo, Thierry Gallouet
We prove a regularity result for weak solutions of nonlinear elliptic problems of the type
-\text{div}(a(x,\nabla u)) = \mu,\ \ u \in W^{1,1}_0(\Omega)
−
div
(
a
(
x
,
∇
u
)
)
=
μ
,
u
∈
W
0
1
,
1
(
Ω
)
using an approximation technique. Here
\mu
μ
is a bounded Radon measure and the operator
A(u) = -\text{div}(a(x,\nabla u))
A
(
u
)
=
−
div
(
a
(
x
,
∇
u
)
)
is assumed to be coercive and monotone, acting between
W^{1,p}_0(\Omega)
W
0
1
,
p
(
Ω
)
and
W^{-1,p'}_0(\Omega)
W
0
−
1
,
p
′
(
Ω
)
.