In this paper, a one-dimensional Euler-Lagrange equation associated with the total variation energy, and Euler-Lagrange equations generated by approximating total variations with linear growth, are considered. Each of the problems presented can be regarded as a governing equation for steady-states in solid-liquid phase transitions. On the basis of precise structural analysis for the solutions, the continuous dependence between the solution classes of approximating problems and that of the limiting Euler-Lagrange equation will be studied by means of the analytical methods of set-valued analysis.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-18,
author = {Ken Shirakawa},
title = {Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies},
journal = {Banach Center Publications},
volume = {86},
year = {2009},
pages = {287-302},
zbl = {1167.35559},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-18}
}
Ken Shirakawa. Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies. Banach Center Publications, Tome 86 (2009) pp. 287-302. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc86-0-18/