The obstacle problem for subelliptic non-divergence form operators on homogeneous groups
Analysis of PDEs
2013-07-17 v1
Abstract
The main result established in this paper is the existence and uniqueness of strong solutions to the obstacle problem for a class of subelliptic operators in non-divergence form. The operators considered are structured on a set of smooth vector fields in R^n; X = \{X_0, X_1, ...,X_q\}, q \le n, satisfying H\"ormanders finite rank condition. In this setting, X_0 is a lower order term while {X1, ...,X_q} are building blocks of the subelliptic part of the operator. In order to prove this, we establish an embedding theorem under the assumption that the set {X_0, X_1, ...,X_q} generates a homogeneous Lie group. Furthermore, we prove that any strong solution belongs to a suitable class of H\"older continuous functions.
Cite
@article{arxiv.1307.4364,
title = {The obstacle problem for subelliptic non-divergence form operators on homogeneous groups},
author = {Marie Frentz and Heather Griffin},
journal= {arXiv preprint arXiv:1307.4364},
year = {2013}
}