An overdetermined elliptic problem in a domain with countably rectifiable boundary

• Autorzy: Przemysław Górka
• Języki publikacji: EN

Abstrakty

EN

We examine an elliptic equation in a domain Ω whose boundary ∂Ω is countably (m-1)-rectifiable. We also assume that ∂Ω 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 Ω is an m-dimensional Euclidean ball.

Kategorie tematyczne

• 28A99: None of the above, but in this section
• 35N99: None of the above, but in this section
• 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 107
• Numer: 1
• Strony: 7-14

Daty

wydano

2007

Twórcy

autor

Przemysław Górka

• Department of Mathematics and Information Sciences, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland

Identyfikatory

DOI

10.4064/cm107-1-2