Advances in Difference Equations
Volume 2006 (2006), Article ID 38121, 14 pages
doi:10.1155/ADE/2006/38121
Basic properties of Sobolev's spaces on time scales
Ravi P. Agarwal1
, Victoria Otero-Espinar2
, Kanishka Perera1
and Dolores R. Vivero2
1Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901, FL, USA
2Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela 15782, Galicia, Spain
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.