Trace and extension theorems for functions of bounded variation
Artikel i vetenskaplig tidskrift, 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).

BV

co-dimension 1 Hausdorff measure

Besov class

extension

metric measure space

Whitney cover

trace

Författare

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

Ämneskategorier

Matematisk analys

DOI

10.2422/2036-2145.201511_007