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
Full text not available from this repository.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 |
| Date Deposited: | 30 Aug 2013 14:29 |
| Last Modified: | 12 Dec 2024 00:26 |
| URI: | http://eprints.lse.ac.uk/id/eprint/52183 |
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