Calibrations and null-Lagrangians for nonlocal perimeters and an application to the viscosity theory
For nonnegative even kernels K, we consider the K-nonlocal perimeter functional acting on sets. Assuming the existence of a foliation of space made of solutions of the associated K-nonlocal mean curvature equation in an open set Ω⊂ℝ�, we built a calibration for the nonlocal perimeter inside Ω⊂ℝ�. Th...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/530728 |
| Acceso en línea: | http://hdl.handle.net/2072/530728 |
| Access Level: | acceso abierto |
| Palabra clave: | Matemàtiques 51 |
| Sumario: | For nonnegative even kernels K, we consider the K-nonlocal perimeter functional acting on sets. Assuming the existence of a foliation of space made of solutions of the associated K-nonlocal mean curvature equation in an open set Ω⊂ℝ�, we built a calibration for the nonlocal perimeter inside Ω⊂ℝ�. The calibrating functional is a nonlocal null-Lagrangian. As a consequence, we conclude the minimality in Ω of each leaf of the foliation. As an application, we prove the minimality of K-nonlocal minimal graphs and that they are the unique minimizers subject to their own exterior data. As a second application of the calibration, we give a simple proof of an important result from the seminal paper of Caffarelli, Roquejoffre, and Savin, stating that minimizers of the fractional perimeter are viscosity solutions. |
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