Traces Of Newton-Sobolev, Haj Lasz-Sobolev, And Bv Functions On Metric Spaces
Annali della Scuola normale superiore di Pisa Classe di scienze(2021)
Abstract
We study the boundary traces of Newton-Sobolev, Haj lasz-Sobolev, 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.
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Key words
Hyperbolic Equations,Parabolic Equations,Integro-Differential Equations,Boundary Value Problems
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