| Title:
|
On mean value properties involving a logarithm-type weight (English) |
| Author:
|
Kuznetsov, Nikolay |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
149 |
| Issue:
|
3 |
| Year:
|
2024 |
| Pages:
|
419-425 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Two new assertions characterizing analytically disks in the Euclidean plane $\mathbb {R}^2$ are proved. Weighted mean value property of positive solutions to the Helmholtz and modified Helmholtz equations are used for this purpose; the weight has a logarithmic singularity. The obtained results are compared with those without weight that were found earlier. (English) |
| Keyword:
|
harmonic function |
| Keyword:
|
Helmholtz equation |
| Keyword:
|
modified Helmholtz equation |
| Keyword:
|
mean value property |
| Keyword:
|
logarithmic weight |
| Keyword:
|
characterization of balls |
| MSC:
|
31A10 |
| MSC:
|
35B05 |
| MSC:
|
35J05 |
| DOI:
|
10.21136/MB.2023.0072-23 |
| . |
| Date available:
|
2024-09-11T13:49:02Z |
| Last updated:
|
2024-09-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152542 |
| . |
| 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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| 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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| Reference:
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| Reference:
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