Plane-like minimizers for a non-local Ginzburg-Landau-type energy in a periodic medium
| Autor: | Matteo Cozzi, Enrico Valdinoci |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
General Mathematics Non-local energies Type (model theory) 01 natural sciences 35A15 plane-like minimizers Mathematics - Analysis of PDEs 0103 physical sciences FOS: Mathematics 0101 mathematics Ginzburg landau Physics 35B65 Plane (geometry) 010102 general mathematics Order (ring theory) 35B08 Non local phase transitions 35R11 Kernel (algebra) 82B26 fractional Laplacian 010307 mathematical physics Fractional Laplacian Energy (signal processing) Analysis of PDEs (math.AP) |
| Zdroj: | Journal de l’École polytechnique — Mathématiques. 4:337-388 |
| ISSN: | 2270-518X |
| DOI: | 10.5802/jep.45 |
| Popis: | where K : Rn × Rn → [0,+∞] is a measurable kernel comparable to that of the fractional Laplacian of order 2s, with s ∈ (0, 1), and W : Rn × R→ [0,+∞) is a smooth double-well potential, with zeroes at u = ±1. Both K and W are assumed to be Zn-periodic. For any vector ω ∈ Rn \{0}, we prove the existence of a minimizer uω of E that is directed along ω and whose interface {|uω| 0. Moreover, uω enjoys a suitable periodicity/almost-periodicity property, in dependence of whether ω is rational or not. As a result, we obtain the existence of plane-like entire solutions to the integro-differential Euler-Lagrange equation corresponding to E . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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