一类二次增长的三角形抛物方程组弱解的处处Hlder连续性

Everywhere Hlder Contiminty for Weak Solutions of a Class of Quadric Increasing Triangular Parabolic Equation Systems

二次增长的非线性抛物方程弱解的正则性研究已有了比较完备的结果,但对于非线性抛物方程组的正则性研究取得的成果还不多,有关文献证明了对角型抛物方程组的弱解在一定条件下是Hlder连续的.本文考虑一类二次增长的三角形抛物方程组utk-Dα[Aαkjβ(z,u)Dβuk+akα(z,u)]=fk(z,u,Du)Akαjβ(z,u)=0,当j>k时k=1,2,…,N z=(x,t)∈Ω×(o,T)∈Rn+1证明了在一定的约束条件下,其弱解是处处HO¨lder连续的.

It has appeared many results about regularity for weak solutions of quadrie increasing parabolic equations. However, there are only a few results about regularity for weak solutions of nonlinear parabolic equation systems. It has been proven in literature that weak solutions of diagonal parabolic equation systems are continuous under a certain condition. Consider a class of nonlinear parabolic equation systems of the form ut^k-Dα[Akj^αβ（z,u）Dβu^k＋αk^α（z,u）]=fk（z,u,Du） Akj^αβ（z,u）=0 ,when j〉k ,where k=1,2,…,N z=（x,t）∈Ω×（o,T）∈R^n＋1 and Ω is a bounded open set in Rn. It is shown that the weak solutions of the class of nonlinear parabolicequation systems are HOlder continuous under the condition, which generalizes the relative results in literature.