Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590126 | Journal of Functional Analysis | 2014 | 39 Pages |
Abstract
In this paper we introduce a new definition of BV based on measure upper gradients and prove the equivalence of this definition, and the coincidence of the corresponding notions of total variation, with the definitions based on relaxation of L1L1 norm of the slope of Lipschitz functions or upper gradients. As in the previous work by the first author with Gigli and Savaré in the Sobolev case, the proof requires neither local compactness nor doubling and Poincaré.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Luigi Ambrosio, Simone Di Marino,