| Autor: |
Giovanni Cupini, Ermanno Lanconelli |
| Jazyk: |
English<br />Italian |
| Rok vydání: |
2024 |
| Předmět: |
|
| Zdroj: |
Bruno Pini Mathematical Analysis Seminar, Vol 14, Iss 2, Pp 129-138 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2240-2829 |
| DOI: |
10.6092/issn.2240-2829/18860 |
| Popis: |
In this article we present some of the main aspects and the most recent results related to the following question: If the surface mean integral of every harmonic function on the boundary of an open set D is "almost'' equal to the value of these functions at x0 in D, then is D "almost'' a ball with center x0? This is the stability counterpart of the rigidity question (the statement above, without the two "almost'') for which several positive answers are known in literature. A positive answer to the stability problem has been given in a paper by Preiss and Toro, by assuming a condition that turns out to be sufficient for ∂D to be geometrically close to a sphere. This condition, however, is not necessary, even for small Lipschitz perturbations of smooth domains, as shown in our recent paper, in which a stability inequality is obtained by assuming only a local regularity property of the boundary of D in at least one of its points closest to x0. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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