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Diversifications of Serrin's and related symmetry problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1316-7913
2012 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, Vol. 57, no 6, 653-665 p.Article in journal (Refereed) Published
Abstract [en]

If D is a bounded C-1 domain (in R-n) for which the solution to the Dirichlet problem Delta u = -1, in D, u = 0 on partial derivative D has the property that, for given constants r, l>40, and for all x is an element of partial derivative D dist(x, Gamma(l)) = r, (Gamma(l) = {u = l}), then D is necessarily a ball. We prove this, and several other related symmetry results, using various known symmetry methods. The novelty of this article lies in the problem(s) rather than in the method(s). We also present (and in some cases also prove) a variety of possible formulations, that diversifies and generalizes Serrin's and other symmetry problems.

Place, publisher, year, edition, pages
2012. Vol. 57, no 6, 653-665 p.
Keyword [en]
overdetermined problem, Serrin-type problem, symmetry
National Category
URN: urn:nbn:se:kth:diva-96182DOI: 10.1080/17476933.2010.504848ISI: 000306169400004ScopusID: 2-s2.0-84859911636OAI: diva2:529935
Swedish Research Council
QC 20120531Available from: 2012-05-31 Created: 2012-05-31 Last updated: 2012-08-06Bibliographically approved

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Shahgholian, Henrik
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