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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.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2018-18
local.scientificprogramResearch in Pairs 2013en_US
local.series.idOWP-2018-18en_US
local.subject.msc35en_US
dc.identifier.urnurn:nbn:de:101:1-2018082111135716053045
dc.identifier.ppn1655292412


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