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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, p. 5002-5041Article 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, p. 5002-5041
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-163520DOI: 10.1016/j.jde.2012.01.032OAI: oai:DiVA.org:uu-163520DiVA, id: diva2:464213
Available from: 2011-12-13 Created: 2011-12-12 Last updated: 2017-12-08Bibliographically approved

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