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The Obstacle Problem for Parabolic Non-divergence Form Operators of Hörmander type
2012 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 252, no 9, 5002-5041 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 RnRn, X={X1,…,Xq}X={X1,…,Xq}, q⩽nq⩽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
2012. Vol. 252, no 9, 5002-5041 p.
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URN: urn:nbn:se:uu:diva-163520DOI: 10.1016/j.jde.2012.01.032OAI: diva2:464213
Available from: 2011-12-13 Created: 2011-12-12 Last updated: 2014-07-18Bibliographically approved

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