The unique continuation property for a nonlinear equation on trees

Mathematics – Analysis of PDEs

Scientific paper

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19 pages and 4 figures

Scientific paper

In this paper we study the game $p-$Laplacian on a tree, that is, $$ u(x)=\frac{\alpha}2{\max_{y\in \S(x)}u(y) + \min_{y\in \S(x)}u(y)} + \frac{\beta}{m}\sum_{y\in \S(x)} u(y), $$ here $x$ is a vertex of the tree and $S(x)$ is the set of successors of $x$. We show, among other properties of the solutions, a characterization 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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