Unique minimizer for a random functional with double-well potential in dimension 1 and 2

Nicolas Dirr, E Orlandi

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We add a random bulk term, modelling the interaction with the impurities of the medium, to a standard functional in the gradient theory of phase transitions consisting of a gradient term with a double well potential. We show that in d >= 2 there exists, for almost all the realizations of the random bulk term, a unique random macroscopic minimizer. This result is in sharp contrast to the case when the random bulk term is absent. In the latter case there are two minimizers which are (in law) invariant under translations in space.
Original languageEnglish
Pages (from-to)331-351
Number of pages21
JournalCommunications in Mathematical Sciences
Volume9
Issue number2
Publication statusPublished - Jun 2011

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