Sourdis, Christos2021-08-192021-08-192021-01-20Sourdis, 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. 1-11.1072-6691https://hdl.handle.net/10877/14401We 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.Text10 pages1 file (.pdf)enAttribution 4.0 InternationalEntire solutionsMonotonicity formulaAllen-Cahn equationLiouville theoremMulti-phase transitionsArticle