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Geometric and energetic criteria for the free boundary regularity in an obstacle-type problem
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2007 (English)In: American Journal of Mathematics, ISSN 0002-9327, E-ISSN 1080-6377, Vol. 129, no 6, 1659-1688 p.Article in journal (Refereed) Published
Abstract [en]

We consider an obstacle-type problem Delta u = f(x)chi(Omega) in D, u = vertical bar del u vertical bar = 0 on D\Omega, where D is a given open set in R-n and Omega is an unknown open subset of D. The problem originates in potential theory, in connection with harmonic continuation of potentials. The qualitative difference between this problem and the classical obstacle problem is that the solutions here are allowed to change sign. Using geometric and energetic criteria in delicate combination we show the C-1,C-1 regularity of the solutions, and the regularity of the free boundary, below the Lipschitz threshold for the right-hand side.

Place, publisher, year, edition, pages
2007. Vol. 129, no 6, 1659-1688 p.
URN: urn:nbn:se:kth:diva-17171ISI: 000251835900007ScopusID: 2-s2.0-38049129462OAI: diva2:335214
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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Shahgholian, Henrik
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