非对角型齐次抛物方程组弱解的正则性

摘要

In this paper ,we first consider the nondiagonal homogeneous parabolic systems related to Hrmander’s vector fields which are free of steps ,and then establish Morrey regularity for gradients of weak solutions and Campanato regularity for weak solutions .Finally Holder regularity for weak solutions is obtained by using isomorphic lemma .%文中考虑由自由到 s步的光滑 Hörmander 向量场构成的非对角型齐次抛物方程组，建立弱解梯度的Morrey正则性和弱解的Campanato正则性，最后利用同构引理得到弱解的Hölder正则性。