We prove an asymptotic monotonicity formula for bounded, globally minimizing solutions (in the sense of Morse) to a class of semilinear elliptic systems of the form , , , with , , nonnegative and vanishing at exactly one point (at least in the closure of the image of the considered solution ). As an application, we can prove a Liouville type theorem under various assumptions.
Submitted January 21, 2019. Published January 20, 2021.
Math Subject Classifications: 35J48, 35J20, 35J61.
Key Words: Entire solutions; monotonicity formula; Allen-Cahn equation; Liouville theorem; multi-phase transitions.
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| Christos Sourdis |
Department of Mathematics
National and Kapodistrian University of Athens
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