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arXiv · 1904.05322

Convex envelopes on Trees

Leandro M. Del Pezzo·Nicolas Frevenza·Julio D. Rossi
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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.

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Leandro M. Del Pezzo, Nicolas Frevenza, Julio D. Rossi. 2019-04-10. Convex envelopes on Trees. https://arxiv.org/abs/1904.05322

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