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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00308730_v259_n1_p1_Acosta |
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todo:paper_00308730_v259_n1_p1_Acosta2023-10-03T14:40:46Z Extension theorems for external cusps with minimal regularity Acosta, G. Ojea, I. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Acosta, G. Ojea, I. 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. |
| format |
JOUR |
| author |
Acosta, G. Ojea, I. |
| author_facet |
Acosta, G. Ojea, I. |
| author_sort |
Acosta, G. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00308730_v259_n1_p1_Acosta |
| work_keys_str_mv |
AT acostag extensiontheoremsforexternalcuspswithminimalregularity AT ojeai extensiontheoremsforexternalcuspswithminimalregularity |
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1807321406856232960 |