The unique continuation property for a nonlinear equation on trees

Abstract

In this paper we study the game $p-$Laplacian on a tree, that is, $$u(x)=\frac{\alpha }{2}\left\{\underset{y\in \S (x)}{\max }u(y)+\underset{y\in \S (x)}{\min }u(y)\right\}+\frac{\beta }{m}\sum _{y\in \S (x)}u(y),$$ 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 $u{\mid }_U=0$ implies $u\equiv 0$.

19 pages and 2 figures, Journal of the London Mathematical Society 2014

References in corpus (2)

• On the problem of unique continuation for the p-Laplace equation
• On a frequency function approach to the unique continuation principle

Cited by in corpus (6)

• On the problem of unique continuation for the p-Laplace equation
• Estimates for Nonlinear Harmonic Measures on Trees
• Dirichlet-to-Neumann maps on Trees
• Systems involving mean value formulas on trees
• The two membranes problem in a regular tree
• Quasiconvex functions on regular trees