抛物型方程解的局部有界性的一个证明

A PROOF FOR THE LOCAL BOUNDEDNESS OF SOLUTIONS OF PARABOLIC EQUATIONS

在１＜ｐ＜２ｎｎ＋２的情形，对下面的抛物型方程，证明解的整体有界性和局部有界性要求不同的条件．在增加ｕ∈Ｌτ（Ｑ），ｌ＞ｎ（２－ｐ）ｐ的假定下。

In case 1< p <2 n /( n +2) the global and local boundedness require different conditions to solutions of the parabolic equation: u t-div (x,t,u,u) + B(x,t,u,u) =0. In this paper a proof is given to the local boundedness by adding the condition u ∈ L ,loc (θ),>n (2- p)/p.