ON A CONJECTURE OF DEGIORGI,E. CONCERNING THE GINZBURG-LANDAU ENERGY

Authors
BREZIS H MIRONESCU P
Citation
H. Brezis et P. Mironescu, ON A CONJECTURE OF DEGIORGI,E. CONCERNING THE GINZBURG-LANDAU ENERGY, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 319(2), 1994, pp. 167-170
Citations number
4
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
319
Issue
2
Year of publication
1994
Pages
167 - 170
Database
ISI
SICI code
0764-4442(1994)319:2<167:OACODC>2.0.ZU;2-Z
Abstract
We consider a family (u(epsilon)) of minimizers of the Ginzburg-Landau energy corresponding to boundary conditions g(epsilon). We assume tha t E(epsilon) (u(epsilon)) less-than-or-equal-to C1 \log epsilon\ + C2 as epsilon --> 0. We prove that (u(epsilon)) may have an oscillatory b ehavior and, in particular, (u(epsilon)) need not converge a.e. This a nswers negatively a question raised by E. De Giorgi.