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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Chengwei Yu & Yue Zeng, 2024. "Local Second Order Sobolev Regularity for p -Laplacian Equation in Semi-Simple Lie Group," Mathematics, MDPI, vol. 12(4), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:601-:d:1340615
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