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arXiv · 1203.3989

The unique continuation property for a nonlinear equation on trees

Leandro M. Del Pezzo·Carolina A. Mosquera·Julio D. Rossi
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Abstract

In this paper we study the game $p-$Laplacian on a tree, that is, $$ u(x)=\fracα2\left\{\max_{y\in §(x)}u(y) + \min_{y\in §(x)}u(y)\right\} + \fracβ{m}\sum_{y\in §(x)} u(y), $$ here $x$ is a vertex of the tree and $S(x)$ is the set of successors of $x$. We study the family of the subsets of the tree that enjoy the unique continuation property, that is, subsets $U$ such that $u\mid_U=0$ implies $u \equiv 0$.

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Leandro M. Del Pezzo, Carolina A. Mosquera, Julio D. Rossi. 2014-01-08. The unique continuation property for a nonlinear equation on trees. https://doi.org/10.1112/jlms%2Fjdt067

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