拟线性抛物型方程广义解的局部有界性

The Local Boundedness for Generalized Solutions of Quasi Linear Parabolic Equations

本文给出了一类较广泛的拟线性抛物型方程广义解的局部有界性,进而也得到了解的Holder连续性.

Denoted by Q=Gx (0,T), the following equation is considered on Q:Where A、B satisfy the following structural conditions: l=2(1+2/n) is the critical exponent admitted by the imbedding theorem and γ can be taken in(1+2/(n+2),2).The local boundedness for the generalized solution of the equation is proved under appropriate inergrability condition for the solution and then the local Holder continuity of the generalized solution follows.