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

Dirr, Nicolas P. ORCID: https://orcid.org/0000-0003-3634-7367 and Orlandi, Enza 2011. Unique minimizer for a random functional with double-well potential in dimension 1 and 2. Communications in Mathematical Sciences 9 (2) , pp. 331-351. 10.4310/CMS.2011.v9.n2.a1

Full text not available from this repository.

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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	International Press
ISSN:	1539-6746
Last Modified:	18 Oct 2022 13:13
URI:	https://orca.cardiff.ac.uk/id/eprint/13073

Citation Data

Cited 2 times in Scopus. View in Scopus. Powered By Scopus® Data

Actions (repository staff only)

Edit Item