Geodesic
Subdifferential decomposition of 1D-regularized total variation with nonhomogeneous coefficients
The Bulletin of Irkutsk State University. Series Mathematics, Tome 36 (2021), pp. 69-83

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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.
Keywords: subdifferential decomposition, nonhomogeneous coefficients, quasilinear equation with singularity. 
@article{IIGUM_2021_36_a5,
     author = {Sh. Kubota},
     title = {Subdifferential decomposition of {1D-regularized} total variation with nonhomogeneous coefficients},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {69--83},
     publisher = {mathdoc},
     volume = {36},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2021_36_a5/}
}
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Sh. Kubota. Subdifferential decomposition of 1D-regularized total variation with nonhomogeneous coefficients. The Bulletin of Irkutsk State University. Series Mathematics, Tome 36 (2021), pp. 69-83. http://geodesic.mathdoc.fr/item/IIGUM_2021_36_a5/