Planelike minimizers of nonlocal Ginzburg-Landau energies and fractional perimeters in periodic media
We consider here a nonlocal phase transition energy in a periodic medium and we construct solutions whose interfaces lie at a bounded distance from any given hyperplane. These solutions are either periodic or quasiperiodic, depending on the rational dependency of the normal direction to the referenc...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/118343 |
| Acceso en línea: | https://hdl.handle.net/2117/118343 https://dx.doi.org/10.1088/1361-6544/aab89d |
| Access Level: | acceso abierto |
| Palabra clave: | Differential equations Mathematical physic Superconductivity Nonlocal Ginzburg-Landau-Allen-Cahn equation Periodic media Density and energy estimates Planelike minimizers Superconductivitat Superconductors Equacions diferencials Física matemàtica Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals Àrees temàtiques de la UPC::Física::Física de l'estat sòlid::Superconductors |
| Sumario: | We consider here a nonlocal phase transition energy in a periodic medium and we construct solutions whose interfaces lie at a bounded distance from any given hyperplane. These solutions are either periodic or quasiperiodic, depending on the rational dependency of the normal direction to the reference hyperplane. Remarkably, the oscillations of the interfaces with respect to the reference hyperplane are bounded by a universal constant times the periodicity scale of the medium. This geometric property allows us to establish, in the limit, the existence of planelike nonlocal minimal surfaces in a periodic structure. The proofs rely on new optimal density and energy estimates. In particular, roughly speaking, the energy of phase transition minimizers is controlled, both from above and below, by the energy of one-dimensional transition layers. |
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