Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion

Marcus, Moshe, and Véron, Laurent. "Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion." Journal of the European Mathematical Society 006.4 (2004): 483-527. <http://eudml.org/doc/277649>.

@article{Marcus2004,
abstract = {Let $\Omega $ be a bounded domain of class $C^2$ in $\mathbb \{R\}^$N and let $K$ be a compact subset of $\partial \Omega $. Assume that $q\ge (N+1)/(N−1)$ and denote by $U_K$ the maximal solution of $−\Delta u+u^q=0$ in $\Omega $ which vanishes on $\partial \Omega \setminus K$. We obtain sharp upper and lower estimates for $U_K$ in terms of the Bessel capacity $C_\{2/q,q^\{\prime \}\}$ and prove that $U_K$ is $\sigma $-moderate. In addition we describe the precise asymptotic behavior of $U_K$ at points $\sigma \in K$, which depends on the “density” of $K$ at $\sigma $, measured in terms of the capacity $C_\{2/q,q^\{\prime \}\}$.},
author = {Marcus, Moshe, Véron, Laurent},
journal = {Journal of the European Mathematical Society},
keywords = {Bessel capacities; maximal solutions; rate of blow-up},
language = {eng},
number = {4},
pages = {483-527},
publisher = {European Mathematical Society Publishing House},
title = {Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion},
url = {http://eudml.org/doc/277649},
volume = {006},
year = {2004},
}

TY - JOUR
AU - Marcus, Moshe
AU - Véron, Laurent
TI - Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion
JO - Journal of the European Mathematical Society
PY - 2004
PB - European Mathematical Society Publishing House
VL - 006
IS - 4
SP - 483
EP - 527
AB - Let $\Omega $ be a bounded domain of class $C^2$ in $\mathbb {R}^$N and let $K$ be a compact subset of $\partial \Omega $. Assume that $q\ge (N+1)/(N−1)$ and denote by $U_K$ the maximal solution of $−\Delta u+u^q=0$ in $\Omega $ which vanishes on $\partial \Omega \setminus K$. We obtain sharp upper and lower estimates for $U_K$ in terms of the Bessel capacity $C_{2/q,q^{\prime }}$ and prove that $U_K$ is $\sigma $-moderate. In addition we describe the precise asymptotic behavior of $U_K$ at points $\sigma \in K$, which depends on the “density” of $K$ at $\sigma $, measured in terms of the capacity $C_{2/q,q^{\prime }}$.
LA - eng
KW - Bessel capacities; maximal solutions; rate of blow-up
UR - http://eudml.org/doc/277649
ER -