The obstacle problem for parabolic non-divergence form operators of Hormander type

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Frentz, Marie¹  Gotmark, Elin¹  Nystrom, Kaj¹ 

[1] Umea Univ, Dept Math & Math Stat, S-90187 Umea, Sweden

关键词: Obstacle problem;    Parabolic equations;    Hormander condition;    Hypo-elliptic;    Embedding theorem;    A priori estimates;   

DOI  :  10.1016/j.jde.2012.01.032

来源: Elsevier

【 摘 要 】

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 R-n, X = {X-1 , . . . , X-q}, q <= n, satisfying Hormander's finite rank condition. We furthermore prove that any strong solution belongs to a suitable class of Holder 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. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free