The Dirichlet problem for superdegenerate differential operators
Analysis of PDEs
2016-09-07 v1
Abstract
Let be an infinitely degenerate second-order linear operator defined on a bounded smooth Euclidean domain. Under weaker conditions than those of H\"ormander, we show that the Dirichlet problem associated with has a unique smooth classical solution. The proof uses the Malliavin calculus. At present, there appears to be no proof of this result using classical analytic techniques.
Cite
@article{arxiv.math/9809186,
title = {The Dirichlet problem for superdegenerate differential operators},
author = {Denis R. Bell and Salah E. -A. Mohammed},
journal= {arXiv preprint arXiv:math/9809186},
year = {2016}
}