Lie Symmetries of Fundamental Solutions to the Leutwiler-Weinstein Equation

Aleksandr V. Aksenov; Heikki Orelma

doi:10.1007/s11118-022-10002-3

Lie Symmetries of Fundamental Solutions to the Leutwiler-Weinstein Equation

Aleksandr V. Aksenov
, Heikki Orelma^*

^*Corresponding author for this work

Computing Sciences

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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 language	English
Pages (from-to)	789-921
Number of pages	33
Journal	Potential Analysis
Volume	59
Issue number	2
Early online date	2022
DOIs	https://doi.org/10.1007/s11118-022-10002-3
Publication status	Published - 2023
Publication type	A1 Journal article-refereed

Funding

This paper was started during a visit by the second author to Moscow State University (MGU). The second author wishes to thank all the nice people at MGU for the inspirational atmosphere and hospitality, and YTK for financial support to complete this job. The authors wish to thank Prof. Sirkka-Liisa Eriksson for her important comments and discussions related to the Dirichlet problem. The authors wishes to thank unknown referees for valuable suggestions and commends.

Keywords

Fundamental solution
Leutwiler-Weinstein equation
Lie symmetries

Publication forum classification

Publication forum level 2

ASJC Scopus subject areas

Analysis

Access to Document

10.1007/s11118-022-10002-3Licence: CC BY

s11118-022-10002-3Final published version, 498 KBLicence: CC BY

https://urn.fi/URN:NBN:fi:tuni-202208176463Licence: CC BY

Cite this

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title = "Lie Symmetries of Fundamental Solutions to the Leutwiler-Weinstein Equation",

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.",

keywords = "Fundamental solution, Leutwiler-Weinstein equation, Lie symmetries",

author = "Aksenov, \{Aleksandr V.\} and Heikki Orelma",

note = "Funding Information: This paper was started during a visit by the second author to Moscow State University (MGU). The second author wishes to thank all the nice people at MGU for the inspirational atmosphere and hospitality, and YTK for financial support to complete this job. The authors wish to thank Prof. Sirkka-Liisa Eriksson for her important comments and discussions related to the Dirichlet problem. The authors wishes to thank unknown referees for valuable suggestions and commends. Publisher Copyright: {\textcopyright} 2022, The Author(s).",

year = "2023",

doi = "10.1007/s11118-022-10002-3",

language = "English",

volume = "59",

pages = "789--921",

journal = "Potential Analysis",

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T1 - Lie Symmetries of Fundamental Solutions to the Leutwiler-Weinstein Equation

AU - Aksenov, Aleksandr V.

AU - Orelma, Heikki

N1 - Funding Information: This paper was started during a visit by the second author to Moscow State University (MGU). The second author wishes to thank all the nice people at MGU for the inspirational atmosphere and hospitality, and YTK for financial support to complete this job. The authors wish to thank Prof. Sirkka-Liisa Eriksson for her important comments and discussions related to the Dirichlet problem. The authors wishes to thank unknown referees for valuable suggestions and commends. Publisher Copyright: © 2022, The Author(s).

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Fundamental solution

KW - Leutwiler-Weinstein equation

KW - Lie symmetries

U2 - 10.1007/s11118-022-10002-3

DO - 10.1007/s11118-022-10002-3

M3 - Article

AN - SCOPUS:85131721341

SN - 0926-2601

VL - 59

SP - 789

EP - 921

JO - Potential Analysis

JF - Potential Analysis

IS - 2

ER -

Lie Symmetries of Fundamental Solutions to the Leutwiler-Weinstein Equation

Abstract

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