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Abstract:

It is known that the classic Korn inequality is not valid for Hölder α domains. In this paper, we prove a family of weaker inequalities for this kind of domains, replacing the standard Lp-norms by weighted norms where the weights are powers of the distance to the boundary. In order to obtain these results we prove first some weighted Poincaré inequalities and then, generalizing an argument of Kondratiev and Oleinik, we show that weighted Korn inequalities can be derived from them. The Poincaré type inequalities proved here improve previously known results. We show by means of examples that our results are optimal. Copyright © 2005 John Wiley & Sons, Ltd.

Registro:

Documento: Artículo
Título:Weighted Poincaré and Korn inequalities for Hölder α domains
Autor:Acosta, G.; Durán, R.G.; Lombardi, A.L.
Filiación:Instituto de Ciencias, Universidad Nacional de General Sarmiento, J. M. Gutierrez 1150, B1613GSX Provincia de Buenos Aires, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
CONICET, Argentina
Palabras clave:Inequalities; Korn inequality; Non-smooth domains; Poincaré; Boundary conditions; Distance measurement; Standards; Inequalities; Korn inequality; Non-smooth domains; Poincaré; Numerical methods
Año:2006
Volumen:29
Número:4
Página de inicio:387
Página de fin:400
DOI: http://dx.doi.org/10.1002/mma.680
Título revista:Mathematical Methods in the Applied Sciences
Título revista abreviado:Math Methods Appl Sci
ISSN:01704214
CODEN:MMSCD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01704214_v29_n4_p387_Acosta

Referencias:

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  • Korn, A., Ubereinige ungleichungen, welche in der theorie der elastischen und elektrischen schwingungen eine rolle spielen (1909) Bulletin Internationale, Cracovie Akademie Umiejet, Classe de Sciences Mathematiques et Naturelles, 3, pp. 705-724
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  • Friedrichs, K.O., On the boundary-value problems of the theory of elasticity and Korn's inequality (1947) Annals of Mathematics, 48, pp. 441-471
  • Kondratiev, V.A., Oleinik, O.A., On Korn's inequalities (1989) Comptes Rendus de L'Academie des Sciences, Paris, 308, pp. 483-487
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Citas:

---------- APA ----------
Acosta, G., Durán, R.G. & Lombardi, A.L. (2006) . Weighted Poincaré and Korn inequalities for Hölder α domains. Mathematical Methods in the Applied Sciences, 29(4), 387-400.
http://dx.doi.org/10.1002/mma.680
---------- CHICAGO ----------
Acosta, G., Durán, R.G., Lombardi, A.L. "Weighted Poincaré and Korn inequalities for Hölder α domains" . Mathematical Methods in the Applied Sciences 29, no. 4 (2006) : 387-400.
http://dx.doi.org/10.1002/mma.680
---------- MLA ----------
Acosta, G., Durán, R.G., Lombardi, A.L. "Weighted Poincaré and Korn inequalities for Hölder α domains" . Mathematical Methods in the Applied Sciences, vol. 29, no. 4, 2006, pp. 387-400.
http://dx.doi.org/10.1002/mma.680
---------- VANCOUVER ----------
Acosta, G., Durán, R.G., Lombardi, A.L. Weighted Poincaré and Korn inequalities for Hölder α domains. Math Methods Appl Sci. 2006;29(4):387-400.
http://dx.doi.org/10.1002/mma.680