Boundary Value Problems
Volume 2010 (2010), Article ID 879821, 12 pages
doi:10.1155/2010/879821
Research Article

Global Optimal Regularity for the Parabolic Polyharmonic Equations

Fengping Yao

Department of Mathematics, Shanghai University, Shanghai 200436, China

Received 21 February 2010; Accepted 3 June 2010

Academic Editor: Vicentiu D. Radulescu

Copyright © 2010 Fengping Yao. 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 show the global regularity estimates for the following parabolic polyharmonic equation ut+(−Δ)mu=f in ℝn×(0,∞),m∈ℤ+ under proper conditions. Moreover, it will be verified that these conditions are necessary for the simplest heat equation ut−Δu=f in ℝn×(0,∞).