Analysis of Total Variation Flow and Its Finite Element Approximations

@inproceedings{Feng2002AnalysisOT,
title={Analysis of Total Variation Flow and Its Finite Element Approximations},
author={Xiaobing Feng and Andreas Prohl},
year={2002}
}

We study the gradient flow for the total variation functional, which arises in image processing and geometric applications. We propose a variational inequality weak formulation for the gradient flow, and establish well-posedness of the problem by the energy method. The main idea of our approach is to exploit the relationship between the regularized gradient flow (characterized by a small positive parameter ε, see (1.7)) and the minimal surface flow [21] and the prescribed mean curvature flow… CONTINUE READING

Trudinger, Elliptic partial differential equations of second order

N.S.D. Gilbarg

Reprint of the 1998 ed • 2001

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Applications to nonlinear partial differential equations and Hamiltonian systems, in Variational methods

M. Struwe

Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics (Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics), • 2000