Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896677 | Journal of Functional Analysis | 2018 | 38 Pages |
Abstract
In this paper we show existence of traces of functions of bounded variation on the boundary of a certain class of domains in metric measure spaces equipped with a doubling measure supporting a 1-Poincaré inequality, and obtain L1 estimates of the trace functions. In contrast with the treatment of traces given in other papers on this subject, the traces we consider do not require knowledge of the function in the exterior of the domain. We also establish a Maz'ya-type inequality for functions of bounded variation that vanish on a set of positive capacity.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
P. Lahti, N. Shanmugalingam,