The unique continuation property for a nonlinear equation on trees

LEANDRO DEL PEZZO, CAROLINA MOSQUERA, JULIO ROSSI

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

OXFORD UNIV PRESS

Lugar: Oxford; Año: 2014 vol. 89 p. 364 - 382

0024-6107

In this paper we study the game $p-$Laplacian on a tree, that is,$u(x)=frac{alpha}2 /left/{max_{y/in S(x)}u(y) + min_{y/in S(x)}u(y) /right/} + /frac{beta}{m}/sum_{y/in S(x)} u(y)$,here $x$ is a vertex of the tree and $S(x)$ is the set of successors of $x$. We study the family of the subsets of the tree that enjoy the unique continuation property, that is, subsets $U$ such that $u=0$ in $U$ implies $u equiv 0$.