An overdetermined elliptic problem in a domain with countably rectifiable boundary

Przemysław Górka. "An overdetermined elliptic problem in a domain with countably rectifiable boundary." Colloquium Mathematicae 107.1 (2007): 7-14. <http://eudml.org/doc/283705>.

@article{PrzemysławGórka2007,
abstract = {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.},
author = {Przemysław Górka},
journal = {Colloquium Mathematicae},
keywords = {countably rectifiable sets; integration by parts; overdetermined problem; potential theory; geometric measure theory},
language = {eng},
number = {1},
pages = {7-14},
title = {An overdetermined elliptic problem in a domain with countably rectifiable boundary},
url = {http://eudml.org/doc/283705},
volume = {107},
year = {2007},
}

TY - JOUR
AU - Przemysław Górka
TI - An overdetermined elliptic problem in a domain with countably rectifiable boundary
JO - Colloquium Mathematicae
PY - 2007
VL - 107
IS - 1
SP - 7
EP - 14
AB - 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.
LA - eng
KW - countably rectifiable sets; integration by parts; overdetermined problem; potential theory; geometric measure theory
UR - http://eudml.org/doc/283705
ER -