Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations
Analysis of PDEs
2019-07-04 v1
Abstract
This paper introduces in a natural way a notion of horizontal convex envelopes of continuous functions in the Heisenberg group. We provide a convexification process to find the envelope in a constructive manner. We also apply the convexification process to show h-convexity of viscosity solutions to a class of fully nonlinear elliptic equations in the Heisenberg group satisfying a certain symmetry condition. Our examples show that in general one cannot expect h-convexity of solutions without the symmetry condition.
Keywords
Cite
@article{arxiv.1907.01701,
title = {Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations},
author = {Qing Liu and Xiaodan Zhou},
journal= {arXiv preprint arXiv:1907.01701},
year = {2019}
}