Electron. J. Differential Equations, Vol. 2021 (2021), No. 04, pp. 111.
An asymptotic monotonicity formula for minimizers of
elliptic systems of AllenCahn type and the Liouville property
Christos Sourdis
Abstract:
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; AllenCahn equation;
Liouville theorem; multiphase transitions.
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Christos Sourdis
Department of Mathematics
National and Kapodistrian University of Athens
Athens, Greece
email: sourdis@uoc.gr

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