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Characterizations for the existence of traces of first-order Sobolev spaces on hyperbolic fillings
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Journal Article
Characterizations for the existence of traces of first-order Sobolev spaces on hyperbolic fillings
2024
Overview
In this paper, we study the existence of traces for Sobolev spaces on the hyperbolic filling
X
of a compact metric space
Z
equipped with a doubling measure. Given a suitable metric on
X
, we can regard
Z
as the boundary of
X
. After equipping
X
with a weighted measure
μ
ρ
via the measure on
Z
and the Euclidean arc length, we give characterizations for the existence of traces for first-order Sobolev spaces.
Publisher
Springer Vienna,Springer Nature B.V
Subject
