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(BV,L p )-decomposition, p = 1,2, of functions in metric random walk spaces

  • José M. Mazón ORCID logo EMAIL logo , Marcos Solera ORCID logo and Julián Toledo ORCID logo
Published/Copyright: November 25, 2020

Abstract

In this paper we study the ( BV , L p ) -decomposition, p = 1 , 2 , of functions in metric random walk spaces, a general workspace that includes weighted graphs and nonlocal models used in image processing. We obtain the Euler-Lagrange equations of the corresponding variational problems and their gradient flows. In the case p = 1 we also study the associated geometric problem and the thresholding parameters describing the behavior of its solutions.


Communicated by Juan Manfredi


Award Identifier / Grant number: PGC2018-094775-B-100

Award Identifier / Grant number: BES-2016-079019

Funding statement: The authors have been partially supported by the Spanish MICIU and FEDER, project PGC2018-094775-B-100. The second author was also supported by the Spanish MICIU under Grant BES-2016-079019, which is also supported by the European FSE.

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Received: 2020-02-03
Revised: 2020-08-31
Accepted: 2020-11-03
Published Online: 2020-11-25
Published in Print: 2022-07-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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