Subdifferential decomposition of 1D-regularized total variation with nonhomogeneous coefficients

TL;DR

This paper analyzes the subdifferential decomposition of a 1D-regularized total variation with nonhomogeneous coefficients, advancing the understanding of singular diffusion and regularity in quasilinear equations relevant to grain boundary motion.

Contribution

It proves a main theorem decomposing the subdifferential into weighted singular and linear diffusions, improving regularity results for singular quasilinear equations.

Findings

Decomposition of subdifferential into weighted singular and linear diffusions.

Enhanced regularity results for quasilinear equations with singularities.

Provides insights applicable to grain boundary motion studies.

Abstract

In this paper, we consider a convex function defined as a 1D-regularized total variation with nonhomogeneous coefficients, and prove the Main Theorem concerned with the decomposition of the subdifferential of this convex function to a weighted singular diffusion and a linear regular diffusion. The Main Theorem will be to enhance the previous regularity result for quasilinear equation with singularity, and moreover, it will be to provide some useful information in the advanced mathematical studies of grain boundary motion, based on KWC type energy.