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.