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 - <p style="text-align: justify;">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 $1&lt;p&lt;2,$ we prove that $∇_{\mathcal{H}}u∈C^α_{{\rm loc}}.$</p>