The Riemann boundary value problem related to the time-harmonic Maxwell equations

Abstract

Abstract In this paper, we first give the definition of Teodorescu operator related to the N $\mathcal{N}$ matrix operator and discuss a series of properties of this operator, such as uniform boundedness, Hölder continuity and so on. Then we propose the Riemann boundary value problem related to the N $\mathcal{N}$ matrix operator. Finally, using the intimate relationship of the corresponding Cauchy-type integral between the N $\mathcal{N}$ matrix operator and the time-harmonic Maxwell equations, we investigate the Riemann boundary value problem related to the time-harmonic Maxwell equations and obtain the integral representation of the solution.

Keywords

• Quaternion analysis
• Riemann boundary value problem
• Time-harmonic Maxwell equations
• Teodorescu operator
• N $\mathcal{N}$ matrix operator