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

Michael Ruzhansky, Durvudkhan Suragan

Research output: Contribution to journalArticle

Abstract

We propose analogues of Green’s and Picone’s identities for the p-sub-Laplacian on stratified Lie groups. In particular, these imply a generalised Díaz-Saá 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.

Original languageEnglish
JournalPotential Analysis
DOIs
Publication statusPublished - Jan 1 2019

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Sub-Laplacian
Comparison Principle
Positive Solution
Picone's Identity
Uniqueness
Heisenberg Group
Euclidean
Analogue
Imply

Keywords

  • Comparison principle
  • Díaz-Saá inequality
  • Green’s identity
  • p-sub-Laplacian
  • Picone’s identity
  • Stratified Lie group

ASJC Scopus subject areas

  • Analysis

Cite this

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