Estimates for nonlinear harmonic measures on trees
Leandro M. Del Pezzo, Carolina A. Mosquera, Julio, D. Rossi · 2016
Abstract. In this paper we give some estimates for nonlinear harmonic measures on trees. In particular, we estimate in terms of the size of a set D the value at the origin of the solution to u(x) = F ((x, 0),..., (x,m−1)) for every x ∈ Tm, a directed tree with m branches with initial datum f + χD. Here F is an averaging operator on Rm, x is a vertex of a directed tree Tm with regular m-branching and (x, i) denotes a successor of that vertex for 0 ≤ i ≤ m − 1. We also provide a characterization of the subsets of the tree for which the unique continuation property holds. 1.