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Regularity of a Parabolic Free Boundary Problem with Holder Continuous Coefficients
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
NTNU, Trondheim, Norway.
2012 (English)In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 37, no 7, 1161-1185 p.Article in journal (Refereed) Published
Abstract [en]

We consider the parabolic obstacle type problem Hu = f chi(Omega) in Q(1)(-), u = vertical bar del u vertical bar = 0 on Q(1)(-)\Omega, where Omega is an unknown open subset of Q(1)(-). This problem has its origin in parabolic potential theory. When f is merely Holder continuous, the usual method based on the use of a monotonicity formula does not apply. Nevertheless, we can, under a combination of energetic and geometric assumptions, prove the optimal C-x(1,1) boolean AND C-t(0,1) regularity of the solution.

Place, publisher, year, edition, pages
2012. Vol. 37, no 7, 1161-1185 p.
Keyword [en]
Free boundary problems, Monotonicity formulas, Obstacle problem
National Category
URN: urn:nbn:se:kth:diva-98958DOI: 10.1080/03605302.2012.683845ISI: 000305248000001ScopusID: 2-s2.0-84862317150OAI: diva2:540512
Knut and Alice Wallenberg Foundation, KAW 2005.0098

QC 20120710

Available from: 2012-07-10 Created: 2012-07-05 Last updated: 2012-09-12Bibliographically approved

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