DOI: 10.68381/jca21011 ISSN: 0944-6532
Multivalued Equations on a Bounded Domain via Minimization on Orlicz-Sobolev Spaces
M. L. Carvalho, J. V. Goncalves
We exploit minimization of locally Lipschitz functionals defined on Orlicz-Sobolev spaces along with convexity techniques, to investigate existence of solution of the multivalued equation
-\Delta_{\Phi} u \in \partial j(.,u) + h
−
Δ
Φ
u
∈
∂
j
(
.
,
u
)
+
h
in
\Omega
Ω
, where
\Omega \subset {\bf R}^N
Ω
⊂
R
N
is a bounded smooth domain,
\Phi: {\bf R} \to [0,\infty)
Φ
:
R
→
[
0
,
∞
)
is an N-function,
\Delta_{\Phi}
Δ
Φ
is the corresponding
\Phi
Φ
-Laplacian,
h
h
is a measure on
\Omega
Ω
and
\partial j(., u)
∂
j
(
.
,
u
)
stands for the Clarke generalized gradient of a function
j
j
linked with critical growth. Regularity of the solutions is addressed as well.