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Weighted Orlicz regularity for fully nonlinear elliptic equations with oblique derivative at the boundary via asymptotic operators
Authors
Junior da S. Bessa
Publication date
11 December 2023
Publisher
View
on
arXiv
Abstract
We prove weighted Orlicz-Sobolev regularity for fully nonlinear elliptic equations with oblique boundary condition under asymptotic conditions of the following problem:
F
(
D
2
u
,
D
u
,
u
,
x
)
=
f
(
x
)
F(D^{2}u,Du,u,x)=f(x)
F
(
D
2
u
,
D
u
,
u
,
x
)
=
f
(
x
)
in the bounded domain
Ω
⊂
R
n
\Omega\subset \mathbb{R}^{n}
Ω
⊂
R
n
(
n
≥
2
n\ge 2
n
≥
2
) and
β
â‹…
D
u
+
γ
u
=
g
\beta\cdot Du+\gamma u= g
β
â‹…
D
u
+
γ
u
=
g
on
∂
Ω
\partial \Omega
∂
Ω
, under suitable assumptions on the source term
f
f
f
, data
β
,
γ
\beta, \gamma
β
,
γ
and
g
g
g
. Our approach guarantees such estimates under conditions where the governing operator
F
F
F
does not require a convex (or concave) structure. We also deal with weighted Orlicz-type estimates for the obstacle problem with oblique derivative condition on the boundary. As a final application, the developed methods provide weighted Orlicz-BMO regularity for the Hessian, provided that the source lies in that space and in weighted Orlicz space associated.Comment: 27 pages. arXiv admin note: substantial text overlap with arXiv:2302.0917
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oai:arXiv.org:2305.11861
Last time updated on 24/05/2023