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) 20362145 (eISSN)
Vol. XVIII 1 313-341Subject Categories
Mathematical Analysis
DOI
10.2422/2036-2145.201511_007