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The obstacle problem for parabolic non-divergence form operators of Hörmander type
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2012 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 252, no 9, 5002-2041 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we establish the existence and uniqueness of strong solutions to the obstacle problem for a class of parabolic sub-elliptic operators in non-divergence form structured on a set of smooth vector fields in Rn, X={X1,…,Xq}X={X1,…,Xq}, q⩽n, satisfying Hörmanderʼs finite rank condition. We furthermore prove that any strong solution belongs to a suitable class of Hölder continuous functions. As part of our argument, and this is of independent interest, we prove a Sobolev type embedding theorem, as well as certain a priori interior estimates, valid in the context of Sobolev spaces defined in terms of the system of vector fields.

Place, publisher, year, edition, pages
Elsevier, 2012. Vol. 252, no 9, 5002-2041 p.
Keyword [en]
obstacle problem, parabolic equations, Hormander condition, hypo-elliptic, embedding theorem, a priori estimates
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-51517DOI: 10.1016/j.jde.2012.01.032ISI: 000301090200014OAI: oai:DiVA.org:umu-51517DiVA: diva2:482990
Note

Originally published in thesis in manuscript form.

Available from: 2012-01-25 Created: 2012-01-24 Last updated: 2017-12-08Bibliographically approved
In thesis
1. Topics on subelliptic parabolic equations structured on Hörmander vector fields
Open this publication in new window or tab >>Topics on subelliptic parabolic equations structured on Hörmander vector fields
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Umeå: Umeå Universitet, 2012. 36 p.
Series
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 51
Keyword
subelliptic, parabolic, obstacle problem, boundary behaviour, weak approximation
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:umu:diva-51604 (URN)978-91-7459-354-9 (ISBN)
Public defence
2012-02-24, Mit-huset, MA121, Umeå Universitet, Umeå, 13:00 (English)
Opponent
Supervisors
Available from: 2012-02-03 Created: 2012-01-27 Last updated: 2012-01-27Bibliographically approved

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Frentz, MarieGötmark, ElinNyström, Kaj
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