关于Heisenberg群上的p-调和逼近定理

On the p-Harmonic Approximation Theorem in the Heisenberg Group

调和逼近引理在偏微分方程组弱解的正则性研究中起着重要作用.本文将经典欧氏空间的p-调和逼近理论发展至非交换Heisenberg群上,为研究Heisenberg群上的次椭圆p-Laplace方程组弱解的最优部分H9lder正则性提供理论基础.

The harmonic approximation theory plays an important role in the study of regularity of weak solutions of PDEs.In this paper,the p-harmonic approximation theory of classical Euclidean spaces is developed to the non-commutative Heisenberg groups,which provides a theoretical basis for further studying the optimal partial H lder regularity of the weak solution for sub-elliptic p-Laplacian systems in the Heisenberg groups.