, Volume 40, Issue 1-3, pp 495-500
Date: 11 Oct 2007

On the maximum principle for linear parabolic equations

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Abstract

We prove extensions of our previous estimates for linear elliptic equations with inhomogeneous terms in L p spaces, pn to linear parabolic equations with inhomogeneous terms in L p , 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.