| Title:
|
Inequalities for surface integrals of non-negative subharmonic functions (English) |
| Author:
|
Aldred, M. P. |
| Author:
|
Armitage, D. H. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
101-113 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let ${\Cal H}$ denote the class of positive harmonic functions on a bounded domain $\Omega$ in $\Bbb R^N$. 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 $u\in {\Cal H}\cap C(\overline{\Omega})$. 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. (English) |
| Keyword:
|
subharmonic |
| Keyword:
|
surface integral |
| MSC:
|
31B05 |
| idZBL:
|
Zbl 0938.31001 |
| idMR:
|
MR1622990 |
| . |
| Date available:
|
2009-01-08T18:39:24Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118990 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| . |
