# Structure of stable solutions of a one-dimensional variational problem

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

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

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topYip, 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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