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Abstract:

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.

Registro:

Documento: Artículo
Título:Extension theorems for external cusps with minimal regularity
Autor:Acosta, G.; Ojea, I.
Filiación:Deptartment of mathematics, University of buenos aires, Ciudad universitaria, Pabellón I, C1428EGA Buenos aires, Argentina
Palabras clave:Extension theorems; External cusp; Weighted sobolev spaces
Año:2012
Volumen:259
Número:1
Página de inicio:1
Página de fin:39
DOI: http://dx.doi.org/10.2140/pjm.2012.259.1
Título revista:Pacific Journal of Mathematics
Título revista abreviado:Pac. J. Math.
ISSN:00308730
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00308730_v259_n1_p1_Acosta

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Citas:

---------- APA ----------
Acosta, G. & Ojea, I. (2012) . Extension theorems for external cusps with minimal regularity. Pacific Journal of Mathematics, 259(1), 1-39.
http://dx.doi.org/10.2140/pjm.2012.259.1
---------- CHICAGO ----------
Acosta, G., Ojea, I. "Extension theorems for external cusps with minimal regularity" . Pacific Journal of Mathematics 259, no. 1 (2012) : 1-39.
http://dx.doi.org/10.2140/pjm.2012.259.1
---------- MLA ----------
Acosta, G., Ojea, I. "Extension theorems for external cusps with minimal regularity" . Pacific Journal of Mathematics, vol. 259, no. 1, 2012, pp. 1-39.
http://dx.doi.org/10.2140/pjm.2012.259.1
---------- VANCOUVER ----------
Acosta, G., Ojea, I. Extension theorems for external cusps with minimal regularity. Pac. J. Math. 2012;259(1):1-39.
http://dx.doi.org/10.2140/pjm.2012.259.1