Delaunay cylinders with constant non-local mean curvature
The aim of this master's thesis is to obtain an alternative proof, using variational techniques, of an existence result for periodic sets in $\mathbb{R}^2$ that minimize a non-local version of the classical perimeter functional adapted to periodic sets. This functional was first introduced by D...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2017 |
| 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:2117/104594 |
| Acceso en línea: | https://hdl.handle.net/2117/104594 |
| Access Level: | acceso abierto |
| Palabra clave: | Differential equations, Elliptic Non-local Delaunay surfaces Fractional perimeter functional Non-local elliptic equation Equacions diferencials el·líptiques Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials |
| Sumario: | The aim of this master's thesis is to obtain an alternative proof, using variational techniques, of an existence result for periodic sets in $\mathbb{R}^2$ that minimize a non-local version of the classical perimeter functional adapted to periodic sets. This functional was first introduced by Dávila, Del Pino, Dipierro and Valdinoci to study periodic sets of codimension 1 in $\mathbb{R}^n$ that are decreasing and cylindrically symmetric in a given direction. Our minimizers are periodic sets of $\mathbb{R}^2$ having constant non-local mean curvature. We call them non-local Delaunay cylinders (or bands) in reference to the classical Delaunay surfaces with constant mean curvature. |
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