Trace and density results on regular trees

TL;DR

This paper characterizes when traces exist for first order Sobolev spaces on regular trees, providing insights into the boundary behavior of functions in these spaces.

Contribution

It introduces new characterizations for the existence of traces in Sobolev spaces on regular trees, advancing understanding of boundary value problems in this setting.

Findings

Provided necessary and sufficient conditions for trace existence

Connected trace properties to geometric features of regular trees

Enhanced the theoretical framework for Sobolev spaces on non-Euclidean structures

Abstract

We give characterizations for the existence of traces for first order Sobolev spaces defined on regular trees.