Journal article
Hausdorff Measure Estimates and Lipschitz Regularity in Inhomogeneous Nonlinear Free Boundary Problems
Archive for rational mechanics and analysis, Vol.213(2), pp.527-559
08/2014
DOI: 10.1007/s00205-014-0739-8
Abstract
In this paper, we prove a Hausdorff measure estimate for the free boundaries of subsolutions of fully nonlinear and quasilinear equations of the type
$${F(D^2u,x)\geqq f(x)}$$
F
(
D
2
u
,
x
)
≧
f
(
x
)
and
$${{\rm div}\,A(x,\nabla u)\geqq \mu}$$
div
A
(
x
,
∇
u
)
≧
μ
where
$${f \in L^{q}, q >N}$$
f
∈
L
q
,
q
>
N
and μ is a signed Radon measure with some appropriate growth condition. Gradient estimates for nonnegative harmonic functions with bounded normal derivatives along the boundary obtained by Caffarelli and Salsa (Geometric Approach to Free Boundary Problems, 2005) are extended to the context of inhomogeneous problems involving fully nonlinear and p-Laplace equations. As an application, Lipschitz regularity is obtained for one phase solutions of inhomogeneous nonlinear free boundary problems.
Details
- Title: Subtitle
- Hausdorff Measure Estimates and Lipschitz Regularity in Inhomogeneous Nonlinear Free Boundary Problems
- Creators
- Diego Moreira - Departamento de Matemática UFC Bloco 914, Campus do Pici Fortaleza Ceará 60455-760 BrazilLihe Wang - Department of Mathematics University of Iowa 14 MacLean Hall Iowa City Iowa 52242-1419 USA
- Resource Type
- Journal article
- Publication Details
- Archive for rational mechanics and analysis, Vol.213(2), pp.527-559
- Publisher
- Springer Berlin Heidelberg
- DOI
- 10.1007/s00205-014-0739-8
- ISSN
- 0003-9527
- eISSN
- 1432-0673
- Language
- English
- Date published
- 08/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9984083292402771
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