Lie Symmetries of Fundamental Solutions to the Leutwiler-Weinstein Equation

Aleksandr V. Aksenov, Heikki Orelma

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

In this article, we study Lie symmetries to fundamental solutions to the Leutwiler-Weinstein equation Lu:=Δu+kxn∂u∂xn+ℓ(xn)2u=0 in the upper half-space ℝ+n. Starting from the infinitesimal generators of the equation Lu = 0, we deduce symmetries of the equation Lu = δ(x − x0), and using its invariant solutions, we construct a fundamental solution. As an application, we study a Green functions of the operator in the hyperbolic unit ball.

Original languageEnglish
Pages (from-to)789-921
Number of pages33
JournalPOTENTIAL ANALYSIS
Volume59
Issue number2
Early online date2022
DOIs
Publication statusPublished - 2023
Publication typeA1 Journal article-refereed

Keywords

  • Fundamental solution
  • Leutwiler-Weinstein equation
  • Lie symmetries

Publication forum classification

  • Publication forum level 2

ASJC Scopus subject areas

  • Analysis

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