Existence of parabolic minimizers to the total variation flow on metric measure spaces

Buffa V, Collins M, Camacho CP (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Manuscripta Mathematica Springer Verlag (Germany)

DOI: 10.1007/s00229-021-01350-2

Abstract

We give an existence proof for variational solutions u associated to the total variation flow. Here, the functions being considered are defined on a metric measure space (X, d, μ) satisfying a doubling condition and supporting a Poincaré inequality. For such parabolic minimizers that coincide with a time-independent Cauchy–Dirichlet datum u on the parabolic boundary of a space-time-cylinder Ω × (0 , T) with Ω ⊂ X an open set and T> 0 , we prove existence in the weak parabolic function space Lw1(0,T;BV(Ω)). In this paper, we generalize results from a previous work by Bögelein, Duzaar and Marcellini by introducing a more abstract notion for BV -valued parabolic function spaces. We argue completely on a variational level.

Authors with CRIS profile

Michael Collins Lehrstuhl für Partial Differential Equations

Involved external institutions

Aalto University Espoo FI Finland (FI)

How to cite

APA:

Buffa, V., Collins, M., & Camacho, C.P. (2022). Existence of parabolic minimizers to the total variation flow on metric measure spaces. Manuscripta Mathematica. https://dx.doi.org/10.1007/s00229-021-01350-2

MLA:

Buffa, Vito, Michael Collins, and Cintia Pacchiano Camacho. "Existence of parabolic minimizers to the total variation flow on metric measure spaces." Manuscripta Mathematica (2022).

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