A LIOUVILLE TYPE RESULT FOR BOUNDED, ENTIRE SOLUTIONS TO A CLASS OF VARIATIONAL SEMILINEAR ELLIPTIC SYSTEMS

摘要

We prove a Liouville type result for bounded, entire solutions to a class of variational semilinear elliptic systems, based on the growth of their potential energy over balls with growing radius. Important special cases to which our result applies are the Ginzburg-Landau system and systems that arise in the study of multi-phase transitions.