Traces of NewtonSobolev, HajlaszSobolev and BV functions on metric spaces
Abstract
We study the boundary traces of NewtonSobolev, HajlaszSobolev, and BV (bounded variation) functions. Assuming less regularity of the domain than is usually done in the literature, we show that all of these function classes achieve the same "boundary values", which in particular implies that the trace spaces coincide provided that they exist. Many of our results seem to be new even in Euclidean spaces but we work in a more general complete metric space equipped with a doubling measure and supporting a Poincare inequality.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.00533
 Bibcode:
 2019arXiv191100533L
 Keywords:

 Mathematics  Metric Geometry;
 Mathematics  Analysis of PDEs;
 Mathematics  Functional Analysis;
 46E35;
 26B30;
 30L99
 EPrint:
 29 pages