# An overdetermined elliptic problem in a domain with countably rectifiable boundary

Colloquium Mathematicae (2007)

- Volume: 107, Issue: 1, page 7-14
- ISSN: 0010-1354

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topPrzemysław 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 -

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