An asymptotic monotonicity formula for minimizers of elliptic systems of Allen-Cahn type and the Liouville property
| Autor: | Christos Sourdis |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Electronic Journal of Differential Equations, Vol 2021, Iss 04,, Pp 1-11 (2021) |
| Druh dokumentu: | article |
| ISSN: | 1072-6691 |
| Popis: | 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 $\Delta u= W_u(u)$, $x\in \mathbb{R}^n$, $n\geq 2$, with $W:\mathbb{R}^m\to \mathbb{R}$, $m\geq 1$, 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. |
| Databáze: | Directory of Open Access Journals |
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