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Pointwise regularity of the free boundary for the parabolic obstacle problem
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4309-9242
2015 (English)In: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 54, no 1, 299-347 p.Article in journal (Refereed) Published
Abstract [en]

We study the parabolic obstacle problem Delta u - u(t) = f chi((u>0)), u >= 0, f is an element of L-p with f(0) = 1 and obtain two monotonicity formulae, one that applies for general free boundary points and one for singular free boundary points. These are used to prove a second order Taylor expansion at singular points (under a pointwise Dini condition), with an estimate of the error (under a pointwise double Dini condition). Moreover, under the assumption that f is Dini continuous, we prove that the set of regular points is locally a (parabolic) C-1-surface and that the set of singular points is locally contained in a union of (parabolic) C-1 manifolds.

Place, publisher, year, edition, pages
2015. Vol. 54, no 1, 299-347 p.
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URN: urn:nbn:se:kth:diva-173421DOI: 10.1007/s00526-014-0787-9ISI: 000359941200012ScopusID: 2-s2.0-84939471926OAI: diva2:853937

QC 20150915

Available from: 2015-09-15 Created: 2015-09-11 Last updated: 2015-09-15Bibliographically approved

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Lindgren, Erik
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