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Abstract:

The Korn inequality and related results on solutions of the divergence in Sobolev spaces have been widely studied since the pioneering works by Korn and Friedrichs. In particular, it is known that this inequality is valid for Lipschitz domains as well as for the more general class of John domains. On the other hand, a few known counterexamples show that those results are not valid for certain bounded domains having external cusps. The goal of this paper is to give very simple counterexamples for a class of cuspidal domains in ℝ n . Moreover, we show that these counterexamples can be used to prove the optimality of recently obtained results involving weighted Sobolev spaces. © 2012 American Mathematical Society.

Registro:

Documento: Artículo
Título:Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates
Autor:Acosta, G.; Durán, R.G.; García, F.L.
Filiación:Departamento de Matemática and IMAS, CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609-2280, United States
Palabras clave:Bad domains; Divergence operator; Korn inequality
Año:2012
Volumen:141
Número:1
Página de inicio:217
Página de fin:232
DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11408-X
Título revista:Proceedings of the American Mathematical Society
Título revista abreviado:Proc. Am. Math. Soc.
ISSN:00029939
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v141_n1_p217_Acosta

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Citas:

---------- APA ----------
Acosta, G., Durán, R.G. & García, F.L. (2012) . Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates. Proceedings of the American Mathematical Society, 141(1), 217-232.
http://dx.doi.org/10.1090/S0002-9939-2012-11408-X
---------- CHICAGO ----------
Acosta, G., Durán, R.G., García, F.L. "Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates" . Proceedings of the American Mathematical Society 141, no. 1 (2012) : 217-232.
http://dx.doi.org/10.1090/S0002-9939-2012-11408-X
---------- MLA ----------
Acosta, G., Durán, R.G., García, F.L. "Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates" . Proceedings of the American Mathematical Society, vol. 141, no. 1, 2012, pp. 217-232.
http://dx.doi.org/10.1090/S0002-9939-2012-11408-X
---------- VANCOUVER ----------
Acosta, G., Durán, R.G., García, F.L. Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates. Proc. Am. Math. Soc. 2012;141(1):217-232.
http://dx.doi.org/10.1090/S0002-9939-2012-11408-X