On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

Abstract:

The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R 2 . Our analysis is based on a suitable operator calculus.

Año de publicación:

2019

Keywords:

• Boundary value problems
• Quaternionic analysis
• Helmholtz equations

Fuente:

scopus