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A free boundary problem in an annulus

Part of: Two-dimensional theory

Published online by Cambridge University Press:  09 April 2009

David E. Tepper
David E. Tepper
Affiliation:
Department of Mathematics Baruch College City University of New YorkNew York, New York 10010, U.S.A.
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Abstract

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If Ω is a ring region with starlike boundary components α and β, then we show for each λ > 0 there exists a ring region ω ⊂ Ω with ∂ ω = α ∪ ϒ, α ∩ ϒ = φ such that there is a harmonic function V in ω satisfying (a) V(z) = 0 for z ∈ α, (b) V(z) = 1 for z ∈ ϒ, (c) | grad V(z)| = λ for z ∈ ϒ ∩ Ω. Furthermore, we show when ω is not equal to Ω; that is, that is, there is a non-trival solution.

MSC classification

Secondary: 31A05: Harmonic, subharmonic, superharmonic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 2 , April 1983 , pp. 177 - 181
Copyright
Copyright © Australian Mathematical Society 1983

References

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