Regularity for p-Harmonic Functions in the Grusin Plane

被引：0

作者：

Yu, Chengwei ^{[1
]}

机构：

[1] Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China

来源：

JOURNAL OF MATHEMATICAL STUDY | 2023年 / 56卷 / 03期

关键词：

p-Laplacian equation; regularities; Grusin plane; QUASI-LINEAR EQUATIONS; METRICS;

D O I：

10.4208/jms.v56n3.23.01

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X={X1,X2} be the orthogonal complement of a Cartan subalgebra in the Gru.sin plane, whose orthonormal basis is formed by the vector fields X1 and X2. When 1< p<8, we prove that weak solutions u to the degenerate subelliptic p-Laplacian equation.X,pu( z)= 2S i= 1 Xi(| Xu| p-2Xiu)= 0 have the C0,1 loc, C1,a loc and W2,2 X, loc -regularities.

引用

页码：219 / 278

页数：60

共 36 条

[1] REGULARITY FOR MINIMIZERS OF NON-QUADRATIC FUNCTIONALS - THE CASE 1-LESS-THAN-P-LESS-THAN-2 [J].

ACERBI, E ;

FUSCO, N .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1989, 140 (01) :115-135

[2]

[Anonymous], 1957, Mem. Accad. Sci. Torino, Cl. Sci. Fis. Mat. Nat.

[3]

Capogna L, 1997, COMMUN PUR APPL MATH, V50, P867, DOI 10.1002/(SICI)1097-0312(199709)50:9<867::AID-CPA3>3.0.CO

[4]

2-3

[5]

Capogna L, 1999, MATH ANN, V313, P263, DOI 10.1007/s002080050261

[6] Conformality and Q-harmonicity in sub-Riemannian manifolds [J].

Capogna, Luca ;

Citti, Giovanna ;

Le Donne, Enrico ;

Ottazzi, Alessandro .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2019, 122 :67-124

[7] Regularity for subelliptic PDE through uniform estimates in multi-scale geometries [J].

Capogna, Luca ;

Citti, Giovanna .

BULLETIN OF MATHEMATICAL SCIENCES, 2016, 6 (02) :173-230

[8] A subelliptic analogue of Aronson-Serrin's Harnack inequality [J].

Capogna, Luca ;

Citti, Giovanna ;

Rea, Garrett .

MATHEMATISCHE ANNALEN, 2013, 357 (03) :1175-1198

[9]

Chow W.L., 1939, Math. Ann., V117, P98

[10] Subelliptic Cordes estimates in the Grusin plane [J].

Di Fazio, G. ;

Domokos, A. ;

Fanciullo, M. S. ;

Manfredi, J. J. .

MANUSCRIPTA MATHEMATICA, 2006, 120 (04) :419-433

← 1 2 3 4 →