The Neumann and Dirichlet problems for the total variation flow in metric measure spaces-Reference-Cited by-同舟云学术

The Neumann and Dirichlet problems for the total variation flow in metric measure spaces

Published:2022-06-29 Issue:0 Volume:0 Page:
ISSN:1864-8258
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Górny Wojciech¹^ORCID,Mazón José M.²^ORCID

Affiliation:

1. Faculty of Mathematics , Universität Wien , Oskar-Morgerstern-Platz 1, 1090 Vienna , Austria ; and Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland

2. Departamento de Anàlisis Matemàtico , Universitat de València , Dr. Moliner 50, 46100 Burjassot , Spain

Abstract

Abstract We study the Neumann and Dirichlet problems for the total variation flow in doubling metric measure spaces supporting a weak Poincaré inequality. We prove existence and uniqueness of weak solutions and study their asymptotic behavior. Furthermore, in the Neumann problem we provide a notion of solutions which is valid for L 1

{L^{1}}

initial data, as well as prove their existence and uniqueness. Our main tools are the first-order linear differential structure due to Gigli and a version of the Gauss–Green formula.

Funder

Austrian Science Fund

Narodowe Centrum Nauki

Ministerio de Ciencia e Innovación

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2021-0107/pdf

Reference35 articles.

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