An asymptotic monotonicity formula for minimizers of elliptic systems of Allen-Cahn type and the Liouville property
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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.
CitationSourdis, C. (2021). An asymptotic monotonicity formula for minimizers of elliptic systems of Allen-Cahn type and the Liouville property. Electronic Journal of Differential Equations, 2021(04), pp. 1-11.
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