Change search
ReferencesLink to record
Permanent link

Direct link
A general class of free boundary problems for fully nonlinear parabolic equations
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
2015 (English)In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 194, no 4, 1123-1134 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we consider the fully nonlinear parabolic free boundary problem { F(D(2)u) - partial derivative(t)u = 1 a.e. in Q(1) boolean AND Omega vertical bar D(2)u vertical bar + vertical bar partial derivative(t)u vertical bar <= K a.e. in Q(1)\Omega, where K > 0 is a positive constant, and Omega is an (unknown) open set. Our main result is the optimal regularity for solutions to this problem: namely, we prove that W-x(2,) (n) boolean AND W-t(1,) (n) solutions are locally C-x(1,) (1) boolean AND C-t(0,) (1) inside Q(1). A key starting point for this result is a new BMO-type estimate, which extends to the parabolic setting the main result in Caffarelli and Huang (Duke Math J 118(1): 1-17, 2003). Once optimal regularity for u is obtained, we also show regularity for the free boundary partial derivative Omega boolean AND Q(1) under the extra condition that Omega superset of{u not equal 0}, and a uniform thickness assumption on the coincidence set {u = 0}.

Place, publisher, year, edition, pages
2015. Vol. 194, no 4, 1123-1134 p.
Keyword [en]
Free boundaries, Regularity, Parabolic fully nonlinear
National Category
URN: urn:nbn:se:kth:diva-173446DOI: 10.1007/s10231-014-0413-7ISI: 000359804400009ScopusID: 2-s2.0-84931568511OAI: diva2:853775

QC 20150915

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

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Shahgholian, Henrik
By organisation
Mathematics (Div.)
In the same journal
Annali di Matematica Pura ed Applicata

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 16 hits
ReferencesLink to record
Permanent link

Direct link