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KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-4309-9242
2015 (English)In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 47, no 3, 1879-1905 p.Article in journal (Refereed) Published
Abstract [en]

We study minimizers of the functional integral(+)(B1) vertical bar del u vertical bar(2)x(n)(a) dx + 2 integral(')(B1)(lambda + u(+) + lambda-u(-)) dx' for a is an element of (- 1, 1). The problem arises in connection with heat flow with control on the boundary. It can also be seen as a nonlocal analogue of the, by now well studied, two-phase obstacle problem. Moreover, when u does not change signs this is equivalent to the fractional obstacle problem. Our main results are the optimal regularity of the minimizer and the separation of the two free boundaries Gamma(+) = partial derivative'{u(center dot, 0) > 0} and Gamma(-) = partial derivative' {u(center dot, 0) < 0} when a >= 0.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2015. Vol. 47, no 3, 1879-1905 p.
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URN: urn:nbn:se:kth:diva-171331DOI: 10.1137/140974195ISI: 000357408600007OAI: diva2:843121

QC 20150727

Available from: 2015-07-27 Created: 2015-07-27 Last updated: 2015-07-27Bibliographically approved

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Lindgren, Erik
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