Traces of Sobolev spaces to irregular subsets of metric measure spaces

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Abstract

Given p∈(1,∞), let (X,d,μ) be a metric measure space with uniformly locally doubling measure μ supporting a weak local (1,p)-Poincaré inequality. For each θ∈[0,p) we characterize the trace space of the Sobolev W1p(X)-space to lower θ-codimensional content regular closed sets S⊂X. In particular, if the space (X,d,μ) is Ahlfors Q-regular for some Q≥1 and p∈(Q,∞), then we obtain an intrinsic description of the trace-space of the Sobolev space W1p(X) to arbitrary closed nonempty sets S⊂X.

About the authors

Alexander Ivanovich Tyulenev

Steklov Mathematical Institute of Russian Academy of Sciences

Author for correspondence.
Email: tyulenev-math@yandex.ru
Candidate of physico-mathematical sciences, Associate professor

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