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$C^{1,α}$-Regularity for $p$-Harmonic Functions in SU(3)

$C^{1,α}$-Regularity for $p$-Harmonic Functions in SU(3)

Year:    2024

Author:    Chengwei Yu

Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 4 : pp. 427–466

Abstract

This artical concerns the $C^{1,α}_{ {\rm loc}}$-regularity of weak solutions $u$ to the degenerate subelliptic $p$-Laplacian equation $$\Delta_{\mathcal{H},p}u(x)=\sum\limits_{i=1}^6X_i^*(|\nabla_{\mathcal{H}}u|^{p-2}X_iu)=0,$$where $\mathcal{H}$ is the orthogonal complement of a Cartan subalgebra in SU(3) with the orthonormal basis composed of the vector fields $X_1,...,X_6.$ When $1<p<2,$ we prove that $∇_{\mathcal{H}}u∈C^α_{{\rm loc}}.$

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v37.n4.5

Journal of Partial Differential Equations, Vol. 37 (2024), Iss. 4 : pp. 427–466

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    40

Keywords:    $p$-Laplacian equation $C^{1 α}$ -regularity SU(3) Caccioppoli inequality De Giorgi $p$-harmonic function.

Author Details

Chengwei Yu