# Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion

Journal of the European Mathematical Society (2004)

- Volume: 006, Issue: 4, page 483-527
- ISSN: 1435-9855

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topMarcus, 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 -

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