We study the dispersive properties of the wave equation associated with the shifted Laplace–Beltrami operator on Damek–Ricci spaces, and deduce Strichartz estimates for a large family of admissible pairs. As an application, we obtain global well–posedness results for the nonlinear wave equation.

The spectrum and the eigenbasis of the Laplace–Beltrami operator on the suspensions of toric automorphisms are investigated. A description in terms of solutions of one-dimensional Schrödinger’s equation is presented. Bibliography: 10 titles. §

Harmonic morphisms are mappings between Riemannian manifolds which preserve Laplace’s equation. They can be characterized as harmonic maps which enjoy an extra property called horizontal weak conformality or semiconformality. We shall give a brief survey of the theory concentrating on (i) twistor methods, (ii) harmonic morphisms with one-dimensional fibres; in particular we shall outline the co...

The eigenvalue problem of the Laplace-Beltrami operators on curved surfaces plays an essential role in the convergence analysis of the numerical simulations of some important geometric partial differential equations which involve this operator. In this note we shall combine the local tangential lifting (LTL) method with the configuration equation to develop a new effective and convergent algori...

Abstract In this work, the Mellin transform method was used to obtain solutions for the stress field components in two dimensional (2D) elasticity problems in terms of plane polar coordinates. the Mellin transformation was applied to the biharmonic stress compatibility equation expressed in terms of the Airy stress potential function, and the boundary value problem transformed to an algebraic  ...

The physical situation which has initiated this research is that of a dielectric particle with electric charges on its surface, placed in electric field. Here, the diffusion equation of the charges is coupled with the Maxwell equations. There is an analytical solution of this system of equation [1] which involves some functional calculus with operators, in particular with Laplace-Beltrami opera...

The Laplace-Beltrami operator is an extension of the Laplacian from flat domains to curved manifolds. It was proven to be useful for color image processing as it models a meaningful coupling between the color channels. This coupling is naturally expressed in the Beltrami framework in which a color image is regarded as a two dimensional manifold embedded in a hybrid, five-dimensional, spatial-ch...

Since the appearance of the paper by Bilal et al. in '91, [1], it has been widely assumed that W –algebras originating from the Hamiltonian reduction of an SL(n, C)-bundle over a Riemann surface give rise to a flat connection, in which the Beltrami differential may be identified. In this letter, it is shown that the use of the Beltrami parametrisation of complex structures on a compact Riemann ...