TY - JOUR
T1 - Regularity for $p$-Harmonic Functions in the Grušin Plane
AU - Yu , Chengwei
JO - Journal of Mathematical Study
VL - 3
SP - 219
EP - 278
PY - 2023
DA - 2023/07
SN - 56
DO - http://doi.org/10.4208/jms.v56n3.23.01
UR - https://global-sci.org/intro/article_detail/jms/21872.html
KW - $p$-Laplacian equation, regularities, Grušin plane.
AB - <div style="text-align: justify;">Let $X=\{X_1,X_2\}$ be the orthogonal complement of a Cartan subalgebra in the Grušin plane, whose orthonormal basis is formed by the vector fields $X_1$ and $X_2$. When $1&lt;p&lt;\infty$, we prove that weak solutions $u$ to the degenerate subelliptic $p$-Laplacian equation $$\triangle_{X,p}u(z)=\sum\limits_{i=1}^2X_i(|Xu|^{p-2}X_iu)=0$$</div><div style="text-align: justify;">have the $C^{0,1}_{loc}$, $C^{1,\alpha}_{loc}$ and $W^{2,2}_{X,loc}$-regularities.</div>