Open Access

Basic properties of Sobolev's spaces on time scales

  • Ravi P Agarwal1Email author,
  • Victoria Otero–Espinar2,
  • Kanishka Perera1 and
  • Dolores R Vivero2
Advances in Difference Equations20062006:038121

https://doi.org/10.1155/ADE/2006/38121

Received: 18 January 2006

Accepted: 22 January 2006

Published: 28 May 2006

Abstract

We study the theory of Sobolev's spaces of functions defined on a closed subinterval of an arbitrary time scale endowed with the Lebesgue Δ-measure; analogous properties to that valid for Sobolev's spaces of functions defined on an arbitrary open interval of the real numbers are derived.

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Authors’ Affiliations

(1)
Department of Mathematical Sciences, Florida Institute of Technology
(2)
Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela

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Copyright

© Ravi P. Agarwal et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.