# Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies

Banach Center Publications (2009)

- Volume: 86, Issue: 1, page 287-302
- ISSN: 0137-6934

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topKen Shirakawa. "Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies." Banach Center Publications 86.1 (2009): 287-302. <http://eudml.org/doc/282537>.

@article{KenShirakawa2009,

abstract = {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.},

author = {Ken Shirakawa},

journal = {Banach Center Publications},

keywords = {Euler–Lagrange equations; structural analysis; continuous dependence of solution classes},

language = {eng},

number = {1},

pages = {287-302},

title = {Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies},

url = {http://eudml.org/doc/282537},

volume = {86},

year = {2009},

}

TY - JOUR

AU - Ken Shirakawa

TI - Continuous dependence for solution classes of Euler-Lagrange equations generated by linear growth energies

JO - Banach Center Publications

PY - 2009

VL - 86

IS - 1

SP - 287

EP - 302

AB - 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.

LA - eng

KW - Euler–Lagrange equations; structural analysis; continuous dependence of solution classes

UR - http://eudml.org/doc/282537

ER -

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