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

Chengwei Yu and Yue Zeng ()
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Chengwei Yu: Department of Basic, China Fire and Rescue Institue, 4 Nanyan Road, Changping District, Beijing 102202, China
Yue Zeng: School of Mathematical Sciences, Beihang University, Haidian District, Beijing 100191, China

Mathematics, 2024, vol. 12, issue 4, 1-14

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 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.

Keywords: structural inequality; W 2,2 -regularity; weak solutions; p -Laplacian equation; semi-simple Lie group; range of p (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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