Vol. 9, No. 7, 2016

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A double well potential system

Jaeyoung Byeon, Piero Montecchiari and Paul H. Rabinowitz

Vol. 9 (2016), No. 7, 1737–1772
DOI: 10.2140/apde.2016.9.1737
Abstract

A semilinear elliptic system of PDEs with a nonlinear term of double well potential type is studied in a cylindrical domain. The existence of solutions heteroclinic to the bottom of the wells as minima of the associated functional is established. Further applications are given, including the existence of multitransition solutions as local minima of the functional.

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Keywords
elliptic system, double well potential, heteroclinic, minimization
Mathematical Subject Classification 2010
Primary: 35J47
Secondary: 35J57, 58E30
Milestones
Received: 23 March 2016
Revised: 26 June 2016
Accepted: 30 July 2016
Published: 7 November 2016
Authors
Jaeyoung Byeon
Department of Mathematical Sciences
KAIST
291 Daehak-ro, Yuseong-gu
Daejeon 305-701
South Korea
Piero Montecchiari
Dipartimento di Ingegneria Civile, Edile e Architettura
Università Politecnica delle Marche
Via brecce bianche
Ancona I-60131
Italy
Paul H. Rabinowitz
Department of Mathematics
University of Wisconsin–Madison
Madison, WI 53706
United States