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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-1-2,
author = {Przemys\l aw G\'orka},
title = {An overdetermined elliptic problem in a domain with countably rectifiable boundary},
journal = {Colloquium Mathematicae},
volume = {107},
year = {2007},
pages = {7-14},
zbl = {1147.35335},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-1-2}
}
Przemysław Górka. An overdetermined elliptic problem in a domain with countably rectifiable boundary. Colloquium Mathematicae, Tome 107 (2007) pp. 7-14. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-1-2/