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Regularity for $p$-Harmonic Functions in the Grušin Plane

Regularity for $p$-Harmonic Functions in the Grušin Plane
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Year:    2023

Author:    Chengwei Yu

Journal of Mathematical Study, Vol. 56 (2023), Iss. 3 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v56n3.23.01

Journal of Mathematical Study, Vol. 56 (2023), Iss. 3 : pp. 219–278

Published online:    2023-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    60

Keywords:    $p$-Laplacian equation regularities Grušin plane.

Author Details

Chengwei Yu