Trace and extension theorems for functions of bounded variation
Journal article, 2018

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, when Ω supports a 1-Poincaré inequality, the trace class of BV(Ω) is L1(∂Ω). We also construct a bounded linear extension from a Besov class of functions on ∂Ω to BV(Ω).

trace

BV

Whitney cover

metric measure space

Besov class

co-dimension 1 Hausdorff measure

extension

Author

Lukas Maly

University of Cincinnati

Nageswari Shanmugalingam

University of Cincinnati

Marie Snipes

Kenyon College, Department of Mathematics and Statistics

Annali della Scuola normale superiore di Pisa - Classe di scienze

0391-173X (ISSN)

Vol. XVIII 1 313-341

Subject Categories

Mathematical Analysis

DOI

10.2422/2036-2145.201511_007

More information

Latest update

3/23/2021