An asymptotic monotonicity formula for minimizers of elliptic systems of Allen-Cahn type and the Liouville property
Date
2021-01-20
Authors
Sourdis, Christos
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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 Δu = Wu(u), x ∈ ℝn, n ≥ 2, with W : ℝ, → ℝ, m ≥ 1, nonnegative and vanishing at exactly one point (at least in the closure of the image of the considered solution u). As an application, we can prove a Liouville type theorem under various assumptions.
Description
Keywords
Entire solutions, Monotonicity formula, Allen-Cahn equation, Liouville theorem, Multi-phase transitions
Citation
Sourdis, C. (2021). An asymptotic monotonicity formula for minimizers of elliptic systems of Allen-Cahn type and the Liouville property. <i>Electronic Journal of Differential Equations, 2021</i>(04), pp. 1-11.