Extension theorems for external cusps with minimal regularity
Sobolev functions defined on certain simple domains with an isolated sin- gular point (such as power type external cusps) can not be extended in standard, but in appropriate weighted spaces. In this article we show that this result holds for a large class of domains that generalizes external cusps,...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2012 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/130092 |
| Acceso en línea: | http://hdl.handle.net/11336/130092 |
| Access Level: | acceso abierto |
| Palabra clave: | EXTENSION THEOREMS EXTERNAL CUSP WEIGHTED SOBOLEV SPACES https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Sobolev functions defined on certain simple domains with an isolated sin- gular point (such as power type external cusps) can not be extended in standard, but in appropriate weighted spaces. In this article we show that this result holds for a large class of domains that generalizes external cusps, allowing minimal boundary regularity. The construction of our extension operator is based on a modification of reflection techniques originally de- veloped for dealing with uniform domains. The weight involved in the ex- tension appears as a consequence of the failure of the domain to comply with basic properties of uniform domains, and it turns out to be a quantification of that failure. We show that weighted, rather than standard spaces, can be treated with our approach for weights that are given by a monotonic function either of the distance to the boundary or of the distance to the tip of the cusp. |
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