A maximum principle for systems with variational structure and an application to standing waves
Nicholas D. Alikakos, Giorgio Fusco · Journal of the European Mathematical Society · 2015
We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a replacement lemma which has as a corollary a maximum principle for minimizers.