Regularity of renormalized solutions to nonlinear elliptic equations away from the support of measure data

@article{DallAglio2019,
abstract = {We prove boundedness and continuity for solutions to the Dirichlet problem for the equation \[ -\{\rm div\}(a(x,\nabla u))=h(x,u)+\mu ,\quad \text\{in\} \ \Omega \subset \mathbb \{R\}^N, \] where the left-hand side is a Leray-Lions operator from $W_0^\{1,p\} (\Omega )$ into $W^\{-1,p^\{\prime \}\}(\Omega )$ with $1<p<N$, $h(x,s)$ is a Carathéodory function which grows like $|s|^\{p-1\}$ and $\mu $ is a finite Radon measure. We prove that renormalized solutions, though not globally bounded, are Hölder-continuous far from the support of $\mu $.},
author = {Dall'Aglio, Andrea, Segura de León, Sergio},
journal = {Czechoslovak Mathematical Journal},
keywords = {bounded solution; $p$-Laplacian; renormalized solution; measure data},
language = {eng},
number = {2},
pages = {379-390},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Regularity of renormalized solutions to nonlinear elliptic equations away from the support of measure data},
url = {http://eudml.org/doc/294765},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Dall'Aglio, Andrea
AU - Segura de León, Sergio
TI - Regularity of renormalized solutions to nonlinear elliptic equations away from the support of measure data
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 2
SP - 379
EP - 390
AB - We prove boundedness and continuity for solutions to the Dirichlet problem for the equation \[ -{\rm div}(a(x,\nabla u))=h(x,u)+\mu ,\quad \text{in} \ \Omega \subset \mathbb {R}^N, \] where the left-hand side is a Leray-Lions operator from $W_0^{1,p} (\Omega )$ into $W^{-1,p^{\prime }}(\Omega )$ with $1<p<N$, $h(x,s)$ is a Carathéodory function which grows like $|s|^{p-1}$ and $\mu $ is a finite Radon measure. We prove that renormalized solutions, though not globally bounded, are Hölder-continuous far from the support of $\mu $.
LA - eng
KW - bounded solution; $p$-Laplacian; renormalized solution; measure data
UR - http://eudml.org/doc/294765
ER -