Abstract and Applied Analysis
Volume 2011 (2011), Article ID 179068, 12 pages
http://dx.doi.org/10.1155/2011/179068
Research Article

Function Spaces with a Random Variable Exponent

Boping Tian, Yongqiang Fu, and Bochi Xu

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 11 February 2011; Accepted 12 April 2011

Academic Editor: Wolfgang Ruess

Copyright © 2011 Boping Tian et al. 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.

Abstract

The spaces with a random variable exponent 𝐿 𝑝 ( 𝜔 ) ( 𝐷 × Ω ) and 𝑊 𝑘 , 𝑝 ( 𝜔 ) ( 𝐷 × Ω ) are introduced. After discussing the properties of the spaces 𝐿 𝑝 ( 𝜔 ) ( 𝐷 × Ω ) and 𝑊 𝑘 , 𝑝 ( 𝜔 ) ( 𝐷 × Ω ) , we give an application of these spaces to the stochastic partial differential equations with random variable growth.