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Volume 37, Issue 4
$C^{1,α}$ -Regularity for $p$-Harmonic Functions in SU(3)

Chengwei YU

DOI: 10.4208/jpde.v37.n4.5

J. Part. Diff. Eq., 37 (2024), pp. 427-466.

Published online: 2024-12

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  • 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 $∇_{\mathcal{H}}u∈C^α_{{\rm loc}}.$

  • Keywords

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

  • AMS Subject Headings

35H20, 35B65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-37-427, author = {YU , Chengwei}, title = {$C^{1,α}$ -Regularity for $p$-Harmonic Functions in SU(3)}, journal = {Journal of Partial Differential Equations}, year = {2024}, volume = {37}, number = {4}, pages = {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 $∇_{\mathcal{H}}u∈C^α_{{\rm loc}}.$

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v37.n4.5}, url = {http://global-sci.org/intro/article_detail/jpde/23690.html} }
TY - JOUR T1 - $C^{1,α}$ -Regularity for $p$-Harmonic Functions in SU(3) AU - YU , Chengwei JO - Journal of Partial Differential Equations VL - 4 SP - 427 EP - 466 PY - 2024 DA - 2024/12 SN - 37 DO - http://doi.org/10.4208/jpde.v37.n4.5 UR - https://global-sci.org/intro/article_detail/jpde/23690.html KW - $p$-Laplacian equation, $C^{1,α}$ -regularity, SU(3), Caccioppoli inequality, De Giorgi, $p$-harmonic function. AB -

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 $∇_{\mathcal{H}}u∈C^α_{{\rm loc}}.$

YU , Chengwei. (2024). $C^{1,α}$ -Regularity for $p$-Harmonic Functions in SU(3). Journal of Partial Differential Equations. 37 (4). 427-466. doi:10.4208/jpde.v37.n4.5
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