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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 797516, 18 pages
http://dx.doi.org/10.1155/2012/797516
Research Article

Regularity for Variational Evolution Integrodifferential Inequalities

1Institute of Liberal Education, Catholic University of Daegu, Daegue 712-702, Republic of Korea
2Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea

Received 8 May 2012; Accepted 28 June 2012

Academic Editor: Sergey Piskarev

Copyright © 2012 Yong Han Kang and Jin-Mun Jeong. 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

We deal with the regularity for solutions of nonlinear functional integrodifferential equations governed by the variational inequality in a Hilbert space. Moreover, by using the simplest definition of interpolation spaces and the known regularity result, we also prove that the solution mapping from the set of initial and forcing data to the state space of solutions is continuous, which very often arises in application. Finally, an example is also given to illustrate our main result.