Convex envelopes on Trees
Analysis of PDEs
2020-11-30 v2
Abstract
We introduce two notions of convexity for an infinite regular tree. For these two notions we show that given a continuous boundary datum there exists a unique convex envelope on the tree and characterize the equation that this envelope satisfies. We also relate the equation with two versions of the Laplacian on the tree. Moreover, for a function defined on the tree, the convex envelope turns out to be the solution to the obstacle problem for this equation.
Keywords
Cite
@article{arxiv.1904.05322,
title = {Convex envelopes on Trees},
author = {Leandro M. Del Pezzo and Nicolas Frevenza and Julio D. Rossi},
journal= {arXiv preprint arXiv:1904.05322},
year = {2020}
}
Comments
24 pages