Geodesic
An overdetermined elliptic problem in a domain with countably rectifiable boundary
Przemys/law G/orka1
1 Department of Mathematics and Information Sciences Warsaw University of Technology Pl. Politechniki 1 00-661 Warszawa, Poland
Colloquium Mathematicum, Tome 107 (2007) no. 1, pp. 7-14 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We examine an elliptic equation in a domain ${\mit\Omega} $ whose boundary $\partial {\mit\Omega} $ is countably $(m-1)$-rectifiable. We also assume that $\partial {\mit\Omega} $ satisfies a geometrical condition. We are interested in an overdetermined boundary value problem (examined by Serrin [Arch. Ration. Mech. Anal. 43 (1971)] for classical solutions on domains with smooth boundary). We show that existence of a solution of this problem implies that ${\mit\Omega} $ is an $m$-dimensional Euclidean ball.
DOI : 10.4064/cm107-1-2
Keywords: examine elliptic equation domain mit omega whose boundary partial mit omega countably m rectifiable assume partial mit omega satisfies geometrical condition interested overdetermined boundary value problem examined serrin arch ration mech anal classical solutions domains smooth boundary existence solution problem implies mit omega m dimensional euclidean ball

Przemys/law G/orka 1

1 Department of Mathematics and Information Sciences Warsaw University of Technology Pl. Politechniki 1 00-661 Warszawa, Poland 
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Przemys/law G/orka. An overdetermined elliptic problem in a domain
 with countably rectifiable boundary. Colloquium Mathematicum, Tome 107 (2007) no. 1, pp. 7-14. doi: 10.4064/cm107-1-2

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