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A derivation theory for generalized Besicovitch spaces and its application for partial differential equations

Published online by Cambridge University Press:  12 July 2007

Juan Casado-Díaz  and
Inmaculada Gayte
Juan Casado-Díaz
Affiliation:
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, C/ Tarifa s/n, Sevilla, CP 41012, Esapaña (jcasado@numer.us.es)
Inmaculada Gayte
Affiliation:
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, C/ Tarifa s/n, Sevilla, CP 41012, Esapaña (gayte@numer.us.es)
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Abstract

We present an extension of Besicovitch spaces, which has its origin in the works of Zhikov et al. and Kozlov and Oleinik. We show that these spaces have a similar behaviour to the Lp spaces, and we give a notion of derivative that allows us to treat partial differential problems in this frame. To the best of our knowledge, this is new, even for the usual Besicovitch spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 2 , April 2002 , pp. 283 - 315
Copyright
Copyright © Royal Society of Edinburgh 2002

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