dc.contributor.author Kawohl, Bernd dc.contributor.author Lucia, Marcello dc.date.accessioned 2018-08-16T11:59:35Z dc.date.available 2018-08-16T11:59:35Z dc.date.issued 2018-08-16 dc.identifier.uri http://publications.mfo.de/handle/mfo/1385 dc.description.abstract We consider the following semilinear overdetermined problem on a two dimensional bounded or unbounded domain $\Omega$ with analytic boundary $\partial\Omega$ having at least one bounded connected component \begin{eqnarray*} \left\{ \begin{array}{l} - \Delta u = g(u) \quad \hbox{in } \Omega,\\ \frac{\partial u}{\partial \nu} =0 \, \hbox{ and } \, u = c \hbox{ on } \partial \Omega, \end{array} \right. \end{eqnarray*} where $c$ is a constant. When $g(c) =0$ the constant solution $u \equiv c$ is the unique solution. For $g(c) \not =0$, we show that the boundary is a circle if and only if the problem admits a solution that has constant third or fourth normal derivative along the boundary. A similar result involving the fifth normal derivative is proved. en_US dc.language.iso en_US en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2018,18 dc.subject Schiffer problem en_US dc.subject Pompeiu problem en_US dc.subject Overdetermined boundary value problem en_US dc.title Some Results Related to Schiffer's Problem en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2018-18 local.scientificprogram Research in Pairs 2013 en_US local.series.id OWP-2018-18 en_US local.subject.msc 35 en_US
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