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| Titel: |
Overdetermined Problems and the <i>p</i>-Laplacian |
| Auteur: |
B. Kawohl |
| Verschenen in: |
Acta mathematica Universitatis Comenianae |
| Paginering: | Jaargang LXXVI (2007) nr. 1 pagina's 77-83 |
| Jaar: |
2007 |
| Inhoud: |
In this lecture I report on essentially two results for overdetermined boundary value problems and the <i>p</i>-Laplace operator. The first one is joint work with H. Shahgholian on Bernoulli type free boundary problems that model for instance galvanization processes. For this family of problems the limits <i>p</i> <FONT SIZE='3' FACE='Symbol'>® ¥</FONT> and<i>p</i> <FONT SIZE='3' FACE='Symbol'>® </FONT> 1 lead to interesting analytical and surprising geometric questions. In particular for the case <i>p</i> <FONT SIZE='3' FACE='Symbol'>® </FONT> 1 I add more recent results, that are not contained in [12]. The second one is joint work with F. Gazzola and I. Fragala [6]. It provides an alternative and more geometric proof of Serrin's seminal symmetry result for positive solutions to overdetermined boundary value problems. As a byproduct I give an analytical proof for the geometric statement that a closed plane curve ofcurvature not exceeding <i>K</i> must enclose a disk of radius 1/<i>K</i>. |
| Uitgever: |
Acta Mathematica Universitatis Comenianae, Institute of Applied Mathematics (provided by DOAJ) |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 43 van 68 gevonden artikelen
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