Journal of Global Optimization

, Volume 40, Issue 1–3, pp 495–500

On the maximum principle for linear parabolic equations

Article

DOI: 10.1007/s10898-007-9249-7

Cite this article as:
Kuo, HJ. & Trudinger, N.S. J Glob Optim (2008) 40: 495. doi:10.1007/s10898-007-9249-7

Abstract

We prove extensions of our previous estimates for linear elliptic equations with inhomogeneous terms in Lp spaces, pn to linear parabolic equations with inhomogeneous terms in Lp, pn  +  1. As with the elliptic case, our results depend on restrictions on parabolicity determined by certain subcones of the positive cone . They also extend the maximum principle of Krylov for the case p  =  n + 1, corresponding to the usual parabolicity.

Keywords

Maximum principles Linear parabolic equations Parabolic Hessian equation Hessian integrals 

Copyright information

© Springer Science+Business Media, LLC. 2007

Authors and Affiliations

  1. 1.Department of Applied MathematicsNational Chung-Hsing UniversityTaichungTaiwan
  2. 2.Centre for Mathematics and its ApplicationsAustralian National UniversityCanberraAustralia

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