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dc.contributor.authorKawohl, Bernd
dc.contributor.authorLucia, Marcello
dc.date.accessioned2018-08-16T11:59:35Z
dc.date.available2018-08-16T11:59:35Z
dc.date.issued2018-08-16
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1385
dc.description.abstractWe 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.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2018,18
dc.subjectSchiffer problemen_US
dc.subjectPompeiu problemen_US
dc.subjectOverdetermined boundary value problemen_US
dc.titleSome Results Related to Schiffer's Problemen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2018-18
local.scientificprogramResearch in Pairs 2013en_US
local.series.idOWP-2018-18en_US
local.subject.msc35en_US


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