摘要
二次增长的抛物型方程弱解的正则性研究已经有了比较完备的结果,但对于方程组弱解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型方程组的弱解在一定条件下是Holder连续的.考虑一类二次增长的三角形抛物方程组 Akjαβ(z,u)=0,当j>k时,k=1,2,…,N, z=(x,t)∈Ω×(0,T) Rn+1证明其弱解是部分Holder连续的,这一结果把有关文献的结果向前推进一步.
It has appeared many results about regularity for weak solutions of quadric increasing parabolic equations. However, there are only a few results about regularity for weak solutions of quadric increasing parabolic equation systems. It has been proven in literature that weak solutions of diagonal parabolic equation systems are continuous under the certain condition. Consider a class of quadric increasing triangular parabolic equation systems of the form fk(z, u, Du), where 1≤K≤N, z=(x, t)∈Ω×(0, T) Rn+1 and Ω is a bounded open set in Rn It is shown that the weak solutions of the class of quadric increasing triangular parabolic equation systems are partial Holder continuous under the certain condition, which generalizes the relative results in literature.
出处
《黑龙江大学自然科学学报》
CAS
2004年第2期31-34,共4页
Journal of Natural Science of Heilongjiang University
关键词
抛物方程组
弱解
正则性
parabolic equation systems
weak solution
regularity
