Extension theorems for external cusps with minimal regularity

Sobolev functions defined on certain simple domains with an isolated singular 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, al...

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Detalles Bibliográficos
Publicado: 2012
Materias:
Extension theorems
External cusp
Weighted sobolev spaces
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00308730_v259_n1_p1_Acosta
http://hdl.handle.net/20.500.12110/paper_00308730_v259_n1_p1_Acosta
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00308730_v259_n1_p1_Acosta
record_format dspace
spelling paper:paper_00308730_v259_n1_p1_Acosta2023-06-08T14:56:34Z Extension theorems for external cusps with minimal regularity Extension theorems External cusp Weighted sobolev spaces Sobolev functions defined on certain simple domains with an isolated singular 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 developed for dealing with uniform domains. The weight involved in the extension 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. © 2012 by Pacific Journal of Mathematics. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00308730_v259_n1_p1_Acosta http://hdl.handle.net/20.500.12110/paper_00308730_v259_n1_p1_Acosta
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Extension theorems
External cusp
Weighted sobolev spaces
spellingShingle Extension theorems
External cusp
Weighted sobolev spaces
Extension theorems for external cusps with minimal regularity
topic_facet Extension theorems
External cusp
Weighted sobolev spaces
description Sobolev functions defined on certain simple domains with an isolated singular 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 developed for dealing with uniform domains. The weight involved in the extension 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. © 2012 by Pacific Journal of Mathematics.
title Extension theorems for external cusps with minimal regularity
title_short Extension theorems for external cusps with minimal regularity
title_full Extension theorems for external cusps with minimal regularity
title_fullStr Extension theorems for external cusps with minimal regularity
title_full_unstemmed Extension theorems for external cusps with minimal regularity
title_sort extension theorems for external cusps with minimal regularity
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00308730_v259_n1_p1_Acosta
http://hdl.handle.net/20.500.12110/paper_00308730_v259_n1_p1_Acosta
_version_ 1768543936186417152

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