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Basic properties of Sobolev's spaces on time scales

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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Correspondence to Ravi P Agarwal.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Agarwal, R.P., Otero–Espinar, V., Perera, K. et al. Basic properties of Sobolev's spaces on time scales. Adv Differ Equ 2006, 038121 (2006). https://doi.org/10.1155/ADE/2006/38121

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

Keywords

  • Differential Equation
  • Real Number
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis