Artículo
Extension theorems for external cusps with minimal regularity
Fecha de publicación:
09/2012
Editorial:
Pacific Journal Mathematics
Revista:
Pacific Journal Of Mathematics
ISSN:
0030-8730
e-ISSN:
1945-5844
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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.
Palabras clave:
EXTENSION THEOREMS
,
EXTERNAL CUSP
,
WEIGHTED SOBOLEV SPACES
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Acosta Rodriguez, Gabriel; Ojea, Ignacio; Extension theorems for external cusps with minimal regularity; Pacific Journal Mathematics; Pacific Journal Of Mathematics; 259; 1; 9-2012; 1-39
Compartir
Altmétricas