This paper considers a wavelet analogue of the classical Ginzburg–Landau energy, where the _H_1 seminorm is replaced by the Besov seminorm defined via an arbitrary regular wavelet. We prove that functionals of this type Γ-converge to a weighted analogue of the TV functional on characteristic functions of finite-perimeter sets. The Γ-limiting functional is defined explicitly, in terms of the wavelet that is used to define the energy. We show that the limiting energy is none other than the surface tension energy in the 2D Wulff problem and its minimizers are represented by the corresponding Wulff shapes. This fact as well as the
1
University of Maryland, College Park, USA
2
University of California Los Angeles, USA
Julia A. Dobrosotskaya; Andrea L. Bertozzi. Wavelet analogue of the Ginzburg–Landau energy and its Γ-convergence. Interfaces and free boundaries, Tome 12 (2010) no. 4, pp. 497-525. doi: 10.4171/ifb/243
@article{10_4171_ifb_243,
author = {Julia A. Dobrosotskaya and Andrea L. Bertozzi},
title = {Wavelet analogue of the {Ginzburg{\textendash}Landau} energy and its {\ensuremath{\Gamma}-convergence}},
journal = {Interfaces and free boundaries},
pages = {497--525},
year = {2010},
volume = {12},
number = {4},
doi = {10.4171/ifb/243},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/243/}
}
TY - JOUR
AU - Julia A. Dobrosotskaya
AU - Andrea L. Bertozzi
TI - Wavelet analogue of the Ginzburg–Landau energy and its Γ-convergence
JO - Interfaces and free boundaries
PY - 2010
SP - 497
EP - 525
VL - 12
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/243/
DO - 10.4171/ifb/243
ID - 10_4171_ifb_243
ER -
%0 Journal Article
%A Julia A. Dobrosotskaya
%A Andrea L. Bertozzi
%T Wavelet analogue of the Ginzburg–Landau energy and its Γ-convergence
%J Interfaces and free boundaries
%D 2010
%P 497-525
%V 12
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/243/
%R 10.4171/ifb/243
%F 10_4171_ifb_243
