Structure of stable solutions of a one-dimensional variational problem

Nung Kwan Yip

ESAIM: Control, Optimisation and Calculus of Variations (2006)

  • Volume: 12, Issue: 4, page 721-751
  • ISSN: 1292-8119

Abstract

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We prove the periodicity of all H2-local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear double well potential function, we make use of explicit solution formulas to analyze the intricate interactions between the phase boundaries. Our analysis can provide insights for tackling the problem with general potential functions.

How to cite

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Yip, Nung Kwan. "Structure of stable solutions of a one-dimensional variational problem." ESAIM: Control, Optimisation and Calculus of Variations 12.4 (2006): 721-751. <http://eudml.org/doc/249615>.

@article{Yip2006,
abstract = { We prove the periodicity of all H2-local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear double well potential function, we make use of explicit solution formulas to analyze the intricate interactions between the phase boundaries. Our analysis can provide insights for tackling the problem with general potential functions. },
author = {Yip, Nung Kwan},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Higher order functional; local minimizer.; higher-order functional; local minimizer},
language = {eng},
month = {10},
number = {4},
pages = {721-751},
publisher = {EDP Sciences},
title = {Structure of stable solutions of a one-dimensional variational problem},
url = {http://eudml.org/doc/249615},
volume = {12},
year = {2006},
}

TY - JOUR
AU - Yip, Nung Kwan
TI - Structure of stable solutions of a one-dimensional variational problem
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2006/10//
PB - EDP Sciences
VL - 12
IS - 4
SP - 721
EP - 751
AB - We prove the periodicity of all H2-local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear double well potential function, we make use of explicit solution formulas to analyze the intricate interactions between the phase boundaries. Our analysis can provide insights for tackling the problem with general potential functions.
LA - eng
KW - Higher order functional; local minimizer.; higher-order functional; local minimizer
UR - http://eudml.org/doc/249615
ER -

References

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