Local Second Order Sobolev Regularity for <i>p</i>-Laplacian Equation in Semi-Simple Lie Group

Abstract

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 X1,…,X2n. When 1p≤4 with n=1 and 1p3+1n−1 with n≥2, we apply the structural inequality to obtain the local horizontal W2,2-regularity of weak solutions to p-Laplacian equation in the semi-simple Lie group. Compared to Euclidean spaces R2n with n≥2, the range of this p obtained is already optimal.

Keywords

• structural inequality
• <i>W</i>^2,2-regularity
• weak solutions
• <i>p</i>-Laplacian equation
• semi-simple Lie group
• range of <i>p</i>