Lipschitz regularity for solutions of the parabolic p-Laplacian in the Heisenberg group

被引：3

作者：

Capogna, Luca ^{[1
]}

Zhong, Xiao ^{[2
]}

Citti, Giovanna ^{[3
,4
,5
,6
]}

机构：

[1] Smith Coll, Dept Math & Stat, Northampton, MA 01060 USA

[2] Univ Helsinki, Dept Math & Stat, Helsinki 00014, Finland

[3] Univ Bologna, Dipartimento Matemat, Piazza Porta S Donato 5, I-40126 Bologna, Italy

[4] Acad Lincei, Ctr Linceo interdisciplinare Beniamino Segre, Rome, Italy

[5] EHESS, CAMS, Paris, France

[6] GNAMPA INDAM, Rome, Italy

来源：

ANNALES FENNICI MATHEMATICI | 2023年 / 48卷 / 02期

基金：

欧盟地平线“2020”; 芬兰科学院;

关键词：

Subelliptic p-Laplacian; parabolic gradient estimates; Heisenberg group; EQUATIONS;

D O I：

10.54330/afm.131227

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove local Lipschitz regularity for weak solutions to a class of degenerate parabolic PDEs modeled on the parabolic p -Laplacian 2 n partial differential tu = X i=1 Xi(| backward difference 0u|p-2Xiu), in a cylinder 11 x R+, where 11 is domain in the Heisenberg group IfI(n, and 2 & LE; p & LE; 4. The result continues to hold in the more general setting of contact subRiemannian manifolds.

引用

页码：411 / 428

页数：18

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