Publications
2002
Issue 32

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

32/2002

An example in the gradient theory of phase transitions

Camillo De Lellis

Abstract

We prove by giving an example that when $n \geq 3$ the asymptotic behavior of functionals $\int_{Ω} ϵ | \nabla^{2} u |^{2} + (1 - | \nabla u |^{2})^{2} / ϵ$ 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 is no longer true in higher dimensions.

Contact the author per mail Download full preprint 150 KB

Received:: 08.04.02

Published:: 08.04.02

MSC Codes:: 49J45, 74G65, 76M30

Keywords:: phase transitions, gamma-convergence, asymptotic analysis, singular perturbations, ginzburg--landau

Related publications

inJournal

2002 Repository Open Access

Camillo De Lellis

An example in the gradient theory of phase transitions

In: Control, optimisation and calculus of variations (ESAIM-COCV), 7 (2002), 285-289 (electronic)

BibTex