Title An example in the gradient theory of phase transitions. Publication Type Journal Article Year of Publication 2002 Authors De Lellis C. Journal ESAIM: Control, Optimisation and Calculus of Variations Volume 7 Pagination 285–289 (electronic) Publisher EDP Sciences Type of Article phase ISSN 1262-3377 Keywords asymptotic analysis, Ginzburg-Landau energy, phase transitions, singular perturbation, \ensuremathΓ-convergence Abstract We prove by giving an example that when n ? 3 the asymptotic behavior of functionals $\int$?[\ensuremathε\ensuremath|?2u\ensuremath|2+(1?\ensuremath|?u\ensuremath|2)2/\ensuremathε] is quite different with respect to the planar case. In particular we show that the one-dimensional ansatz due to Aviles and Giga in the planar case (see Aviles and Giga 1987) is no longer true in higher dimensions. Notes ESAIM Control Optim. Calc. Var. 7 (2002), 285–289 URL https://www.esaim-cocv.org/articles/cocv/abs/2002/01/cocvVol7-12/cocvVol7-12.html DOI 10.1051/cocv:2002012
PDF:
Order:
2