Lipschitz continuity and convexity preserving for solutions of semilinear evolution equations in the Heisenberg group
Analysis of PDEs
2016-04-05 v2
Abstract
In this paper we study viscosity solutions of semilinear parabolic equations in the Heisenberg group. We show uniqueness of viscosity solutions with exponential growth at space infinity. We also study Lipschitz and horizontal convexity preserving properties under appropriate assumptions. Counterexamples show that in general such properties that are well-known for semilinear and fully nonlinear parabolic equations in the Euclidean spaces do not hold in the Heisenberg group.
Keywords
Cite
@article{arxiv.1603.08986,
title = {Lipschitz continuity and convexity preserving for solutions of semilinear evolution equations in the Heisenberg group},
author = {Qing Liu and Juan Manfredi and Xiaodan Zhou},
journal= {arXiv preprint arXiv:1603.08986},
year = {2016}
}