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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Frentz, Marie

关键词: Obstacle problem;    Parabolic equations;    Hormander condition;    Hypoelliptic;    Regularity;   

DOI  :  10.1016/j.jde.2013.07.055

来源: Elsevier

【 摘 要 】

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,..., X-q} in R-n with C-infinity-coefficients satisfying Hormander's finite rank condition, i.e., the rank of Lie[X-1,..., X-q] equals n at every point in R-n. 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 = (R-n, o, delta(lambda)) such that X-1,..., X-q are left translation invariant on G and such that X-1,..., X-q are delta(lambda)-homogeneous of degree one. (C) 2013 Elsevier Inc. All rights reserved.

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