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Regularity of a free boundary with application to the Pompeiu problem
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-1316-7913
2000 (English)In: Annals of Mathematics, ISSN 0003-486X, E-ISSN 1939-8980, Vol. 151, no 1, 269-292 p.Article in journal (Refereed) Published
Abstract [en]

In the unit ball B(0, 1), let u and Omega (a domain in R-N) salve the following overdetermined problem: Delta u = chi(Omega) in B(0, 1), 0 is an element of partial derivative Omega, u = \del u\ = 0 in B(0, 1) \ Omega, where chi(Omega) denotes the characteristic function, and the equation is satisfied in the sense of distributions. If the complement of Omega does not develop cusp singularities at the origin then we prove partial derivative Omega is analytic in some small neighborhood of the origin. The result can be modified to yield for more general divergence form operators. As an application of this, then, we obtain the regularity of the boundary of a domain without the Pompeiu property, provided its complement has no cusp singularities.

Place, publisher, year, edition, pages
2000. Vol. 151, no 1, 269-292 p.
Keyword [en]
quadrature domains, dimensions, spheres, growth
URN: urn:nbn:se:kth:diva-19609ISI: 000085778300008OAI: diva2:338301
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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