Local Second Order Sobolev Regularity for p -Laplacian Equation in Semi-Simple Lie Group.

In this paper, we establish a structural inequality of the ∞-subLaplacian ▵ 0 , ∞ in a class of the semi-simple Lie group endowed with the horizontal vector fields X 1 , ... , X 2 n . When 1 < p ≤ 4 with n = 1 and 1 < p < 3 + 1 n − 1 with n ≥ 2 , we apply the structural inequality to obtain the local horizontal W 2 , 2 -regularity of weak solutions to p-Laplacian equation in the semi-simple Lie group. Compared to Euclidean spaces R 2 n with n ≥ 2 , the range of this p obtained is already optimal. [ABSTRACT FROM AUTHOR]