Regularity for $p$-Harmonic Functions in the Grušin Plane
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@Article{JMS-56-219,
author = {Yu , Chengwei},
title = {Regularity for $p$-Harmonic Functions in the Grušin Plane},
journal = {Journal of Mathematical Study},
year = {2023},
volume = {56},
number = {3},
pages = {219--278},
abstract = {
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 $1<p<\infty$, we prove that weak solutions $u$ to the degenerate subelliptic $p$-Laplacian equation $$\triangle_{X,p}u(z)=\sum\limits_{i=1}^2X_i(|Xu|^{p-2}X_iu)=0$$
have the $C^{0,1}_{loc}$, $C^{1,\alpha}_{loc}$ and $W^{2,2}_{X,loc}$-regularities.
},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v56n3.23.01},
url = {http://global-sci.org/intro/article_detail/jms/21872.html}
}
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 -
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 $1<p<\infty$, we prove that weak solutions $u$ to the degenerate subelliptic $p$-Laplacian equation $$\triangle_{X,p}u(z)=\sum\limits_{i=1}^2X_i(|Xu|^{p-2}X_iu)=0$$
have the $C^{0,1}_{loc}$, $C^{1,\alpha}_{loc}$ and $W^{2,2}_{X,loc}$-regularities.
Chengwei Yu. (2023). Regularity for $p$-Harmonic Functions in the Grušin Plane.
Journal of Mathematical Study. 56 (3).
219-278.
doi:10.4208/jms.v56n3.23.01
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