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Publication 11-CNA-003

Characterization of Sobolev and BV Space

Giovanni Leoni
Carnegie Mellon University
Department of Mathematical Sciences
Pittsburgh, PA 15213
giovanni@andrew.cmu.edu

Daniel Spector
Carngie Mellon University
Department of Mathematical Sciences
Pittsburgh, PA 15213
dspector@andrew.cmu.edu

 

Abstract: The main results of this paper are new characterizations of $ W^{1,p}(\Omega)$, $ 1<p<\infty$, and $ BV(\Omega)$ for $ \Omega \subset \mathbb{R}^N$ an arbitrary open set. Using these results, we answer some open questions of Brezis and Ponce.

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