The unique continuation property for a nonlinear equation on trees

LEANDRO DEL PEZZO, CAROLINA MOSQUERA, JULIO ROSSI

Córdoba, Prov. de Córdoba

Congreso; IV Congreso Latinoamericano de Matemáticos; 2012

In this work we study the game $p-$Laplacian on a tree, that is,[u(x)=rac{alpha}2left{max_{yin mathcal{S}(x)}u(y) + min_{yinS(x)}u(y) ight} + rac{eta}{m}sum_{yin S(x)} u(y),]here $x$ is a vertex of the $m$-branches directed tree $T_m$ and $S(x)$ is the set ofsuccessors 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 $umid_U=0$implies $u equiv 0$.