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Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a $p$-Poincar\'e inequality by Eriksson-Bique, Sylvester; Gibara, Ryan; Korte, Riikka; Shanmugalingam, Nageswari is a scholarly article available to read on EtoBox.

What is Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a $p$-Poincar\'e inequality about?

We consider the question of whether a domain with uniformly thick boundary at all locations and at all scales has a large portion of its boundary visible from the interior; here, "visibility" indicates the existence of John curves connecting the interior point to the points on the "visible boundary". In this paper, we provide an affirmative answer in the setting of a doubling metric measure space supporting a $p$-Poincar\'e inequality for $1<p<\infty$, thus extending the results of [20,2,9] to non-Ahlfors regular spaces. We show that $t$-codimensional thickness of the boundary for $0<t<p$ implies $p$-codimensional thickness of the visible boundary. For such domains we prove that traces of Sobolev functions on the domain belong to the Besov class of the visible boundary.

Author

Eriksson-Bique, Sylvester; Gibara, Ryan; Korte, Riikka; Shanmugalingam, Nageswari

Published

2023

Language

EN