Convex Envelopes on Trees
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...
| Authors: | , , |
|---|---|
| Format: | article |
| Status: | Published version |
| Publication Date: | 2020 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/136901 |
| Online Access: | http://hdl.handle.net/11336/136901 |
| Access Level: | Open access |
| Keyword: | CONVEXITY ON GRAPHS LAPLACIAN ON GRAPHS CONVEX ENVELOPES https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Summary: | 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. |
|---|