Coupled second order singular perturbations for phase transitions

Margarida Baía; Ana Cristina Barroso; Milena Chermisi; José Matias

doi:10.1088/0951-7715/26/5/1271

Nonlinearity

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Paper

Coupled second order singular perturbations for phase transitions

Margarida Baía¹, Ana Cristina Barroso², Milena Chermisi³ and José Matias¹

Published 10 April 2013 • 2013 IOP Publishing Ltd & London Mathematical Society
Nonlinearity, Volume 26, Number 5

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Author e-mails

mbaia@math.ist.utl.pt

abarroso@ptmat.fc.ul.pt

Milena.Chermisi@fmc-ag.com

jmatias@math.ist.utl.pt

Author affiliations

¹ Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisbon, Portugal

² Universidade de Lisboa, Faculdade de Ciências and CMAF, Av. Prof. Gama Pinto 2, 1649-003 Lisbon, Portugal

³ Fresenius Medical Care, Via Crema, 8 - Palazzo Pignano 26020 (CR) Italy

Dates

Received 14 May 2012
In final form 17 May 2012
Published 10 April 2013

Citation

Margarida Baía et al 2013 Nonlinearity 26 1271

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DOI

https://doi.org/10.1088/0951-7715/26/5/1271

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Abstract

The asymptotic behaviour of a family of singular perturbations of a non-convex second order functional of the type

$\begin{equation*}\int_\Omega f(x,u(x),\nabla u(x), \nabla^2 u(x)) \, \rmd x \end{equation*}$

is studied through Γ-convergence techniques as a variational model to address two-phase transition problems.

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