An asymptotic monotonicity formula for minimizers of elliptic systems of Allen-Cahn type and the Liouville property
| dc.contributor.author | Sourdis, Christos | |
| dc.date.accessioned | 2021-08-19T19:29:17Z | |
| dc.date.available | 2021-08-19T19:29:17Z | |
| dc.date.issued | 2021-01-20 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 10 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14401 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Entire solutions | |
| dc.subject | Monotonicity formula | |
| dc.subject | Allen-Cahn equation | |
| dc.subject | Liouville theorem | |
| dc.subject | Multi-phase transitions | |
| dc.title | An asymptotic monotonicity formula for minimizers of elliptic systems of Allen-Cahn type and the Liouville property | en_US |
| dc.type | Article |