一类Heisenberg群上的非线性方程的解之弱可微性

Weak Differentiability of Solutions for Nonlinear Sub-elliptic Equations in the Heisenberg Group

该文利用分数阶差商和先验估计 ,证明一类Heisenberg群上的非线性次椭圆方程的W2 ,2 -弱可微性。这类问题是欧氏空间上的偏微分方程在一般度量空间上的发展 ,在几何控制与数学物理中有着非常重要的应用。

With the help of fractional difference quotients, the W 2,2 -weak differentiability of solutions for a nonlinear sub-elliptic equation in the Heisenberg group is established. This is a generalization of theory for partial differential equations in Euclidean spaces to that of general metric spaces. There are many important applications in geometrical control theory and mathematical physics.