Trace and extension theorems for functions of bounded variation

2015/11/14 by Malý, Lukáš, Shanmugalingam, Nageswari, Snipes, Marie · 2 citations
#26A45 #26B30 #30L99 #31E05 (Secondary) #46E35 (Primary) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1511.04503

Abstract

In this paper we show that every L¹-integrable function on ∂Ω can be obtained as the trace of a function of bounded variation in Ω whenever Ω is a domain with regular boundary ∂Ω in a doubling metric measure space. In particular, the trace class of BV(Ω) is L¹(∂Ω) provided that Ω supports a 1-Poincaré inequality. We also construct a bounded linear extension from a Besov class of functions on ∂Ω to BV(Ω).

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• Trace and Extension Theorems for Besov Functions in Doubling Metric Measure Spaces
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