Electron. J. Differential Equations, Vol. 2022 (2022), No. 27, pp. 1-15.

Second order Sobolev regularity for p-harmonic functions in SU(3)

Chengwei Yu

Abstract:
Let u be a weak solution to the degenerate subelliptic p-Laplacian equation

where $\mathcal{H}$ is the orthogonal complement of a Cartan subalgebra in SU(3) and its orthonormal basis is composed of the vector fields X1,...,X6. We prove that when 1<p<7/2, the solution u has the second order horizontal Sobolev $W^{2,2}_{\mathcal{H},\rm loc}$ -regularity.

Submitted December 2, 2021. Published April 6, 2022.
Math Subject Classifications: 35H20, 35B65.
Key Words: p-Laplacian equation; SU(3); $W^{2,2}_{\mathcal{H},\rm loc}$-regularity; Hessian matrix; p-harmonic function.
DOI: https://doi.org/10.58997/ejde.2022.27

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Chengwei Yu
School of Mathematical Sciences
Beihang University
Haidian District, Beijing 100191, China
email: chengweiyu@buaa.edu.cn

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