Inequalities for surface integrals of non-negative subharmonic functions

Aldred, M. P., and Armitage, David H.. "Inequalities for surface integrals of non-negative subharmonic functions." Commentationes Mathematicae Universitatis Carolinae 39.1 (1998): 101-113. <http://eudml.org/doc/248267>.

@article{Aldred1998,
abstract = {Let $\{\mathcal \{H\}\}$ denote the class of positive harmonic functions on a bounded domain $\Omega $ in $\mathbb \{R\}^N$. Let $S$ be a sphere contained in $\overline\{\Omega \}$, and let $\sigma $ denote the $(N-1)$-dimensional measure. We give a condition on $\Omega $ which guarantees that there exists a constant $K$, depending only on $\Omega $ and $S$, such that $\int _Su\,d\sigma \le K\int _\{\partial \Omega \}u\,d\sigma $ for every $u\in \{\mathcal \{H\}\}\cap C(\overline\{\Omega \})$. If this inequality holds for every such $u$, then it also holds for a large class of non-negative subharmonic functions. For certain types of domains explicit values for $K$ are given. In particular the classical value $K=2$ for convex domains is slightly improved.},
author = {Aldred, M. P., Armitage, David H.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {subharmonic; surface integral; subharmonic function; surface integral},
language = {eng},
number = {1},
pages = {101-113},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Inequalities for surface integrals of non-negative subharmonic functions},
url = {http://eudml.org/doc/248267},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Aldred, M. P.
AU - Armitage, David H.
TI - Inequalities for surface integrals of non-negative subharmonic functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 1
SP - 101
EP - 113
AB - Let ${\mathcal {H}}$ denote the class of positive harmonic functions on a bounded domain $\Omega $ in $\mathbb {R}^N$. Let $S$ be a sphere contained in $\overline{\Omega }$, and let $\sigma $ denote the $(N-1)$-dimensional measure. We give a condition on $\Omega $ which guarantees that there exists a constant $K$, depending only on $\Omega $ and $S$, such that $\int _Su\,d\sigma \le K\int _{\partial \Omega }u\,d\sigma $ for every $u\in {\mathcal {H}}\cap C(\overline{\Omega })$. If this inequality holds for every such $u$, then it also holds for a large class of non-negative subharmonic functions. For certain types of domains explicit values for $K$ are given. In particular the classical value $K=2$ for convex domains is slightly improved.
LA - eng
KW - subharmonic; surface integral; subharmonic function; surface integral
UR - http://eudml.org/doc/248267
ER -