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Regularity in the obstacle problem for parabolic non-divergence operators of Hörmander type

Frentz, Marie (2013) Regularity in the obstacle problem for parabolic non-divergence operators of Hörmander type. Journal of Differential Equations, 255 (10). pp. 3638-3677. ISSN 0022-0396

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Identification Number: 10.1016/j.jde.2013.07.055

Abstract

In this paper we continue the study initiated in [15] concerning the obstacle problem for a class of parabolic non-divergence operators structured on a set of vector fields X = {X1, ..., Xq} in Rn with C∞-coefficients satisfying Hörmander's finite rank condition, i.e., the rank of Lie [X1, ..., Xq] equals n at every point in Rn. In [15] we proved, under appropriate assumptions on the operator and the obstacle, the existence and uniqueness of strong solutions to a general obstacle problem. The main result of this paper is that we establish further regularity, in the interior as well as at the initial state, of strong solutions. Compared to [15] we in this paper assume, in addition, that there exists a homogeneous Lie group G = (Rn, {ring operator}, δλ) such that X1, ..., Xq are left translation invariant on G and such that X1, ..., Xq are δλ-homogeneous of degree one.

Item Type: Article
Official URL: http://www.journals.elsevier.com/journal-of-differ...
Additional Information: © 2013 Elsevier B.V.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 30 Aug 2013 14:29
Last Modified: 30 Jan 2019 19:15
URI: http://eprints.lse.ac.uk/id/eprint/52183

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