Green's Identities, Comparison Principle and Uniqueness of Positive Solutions for Nonlinearp-sub-Laplacian Equations on Stratified Lie Groups

被引：5

作者：

Ruzhansky, Michael ^{[1
,2
]}

Suragan, Durvudkhan ^{[3
]}

机构：

[1] Univ Ghent, Dept Math Anal Log & Discrete Math, Ghent, Belgium

[2] Queen Mary Univ London, Sch Math Sci, Bethnal Green, England

[3] Nazarbayev Univ, Dept Math, Nur Sultan, Kazakhstan

来源：

POTENTIAL ANALYSIS | 2020年 / 53卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

p-sub-Laplacian; Green's identity; Picone's identity; Diaz-Saa inequality; Comparison principle; Stratified Lie group; HEISENBERG-GROUP; INEQUALITIES; THEOREM; SPACES;

D O I：

10.1007/s11118-019-09782-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We propose analogues of Green's and Picone's identities for thep-sub-Laplacian on stratified Lie groups. In particular, these imply a generalised Diaz-Saa inequality. Using these we derive a comparison principle and uniqueness of positive solutions to nonlinear hypoelliptic equations on general stratified Lie groups extending to this setting previously known results on Euclidean and Heisenberg groups.

引用

页码：645 / 658

页数：14

共 20 条

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