Regularity of a Parabolic Free Boundary Problem with Holder Continuous Coefficients
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
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.
Free boundary problems, Monotonicity formulas, Obstacle problem
IdentifiersURN: urn:nbn:se:kth:diva-98958DOI: 10.1080/03605302.2012.683845ISI: 000305248000001ScopusID: 2-s2.0-84862317150OAI: oai:DiVA.org:kth-98958DiVA: diva2:540512
FunderKnut and Alice Wallenberg Foundation, KAW 2005.0098
QC 201207102012-07-102012-07-052012-09-12Bibliographically approved