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

Dall'Aglio, Andrea, and Segura de León, Sergio. "Regularity of renormalized solutions to nonlinear elliptic equations away from the support of measure data." Czechoslovak Mathematical Journal 69.2 (2019): 379-390. <http://eudml.org/doc/294765>.

@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 -