ASYMPTOTIC BEHAVIOR OF THE FREE INTERFACE FOR ENTIRE VECTOR MINIMIZERS IN PHASE TRANSITIONS
We study globally bounded entire minimizers u : Rn → Rm of Allen-Cahn systems for potentials W ≥ 0 with {W = 0}= {a1, ..., aN } and W (u) ∼ |u− ai|α near u = ai, 0 < α < 2. Such solutions are, over large regions, identically equal to some zeroes of the potential ai’s. We establish the estimate...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1996 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/1996 |
| Access Level: | acceso abierto |
| Sumario: | We study globally bounded entire minimizers u : Rn → Rm of Allen-Cahn systems for potentials W ≥ 0 with {W = 0}= {a1, ..., aN } and W (u) ∼ |u− ai|α near u = ai, 0 < α < 2. Such solutions are, over large regions, identically equal to some zeroes of the potential ai’s. We establish the estimates Ln(I0 ∩ Br (x0)) ≤ c1r n−1 , Hn−1(∂∗I0 ∩ Br (x0)) ≥ c2r n−1 , r ≥ r0(x0) for the diffuse interface I0 := {x ∈ Rn : min1≤i≤N |u(x)− ai | > 0} and the free boundary ∂I0. Furthermore, if α = 1 we establish the upper bound Hn−1(∂∗I0 ∩ Br (x0)) ≤ c3r n−1 , r ≥ r0(x0). |
|---|