Regularization of a continuation problem for electrodynamic equations

Abstract

Abstract The problem of continuation of a solution of electrodynamic equations from the time-like half-plane S = { x ∈ R 3 ∣ x 3 = 0 } S=\{x\in\mathbb{R}^{3}\mid x_{3}=0\} inside the half-space R + 3 = { x ∈ R 3 ∣ x 3 > 0 } \mathbb{R}^{3}_{+}=\{x\in\mathbb{R}^{3}\mid x_{3}>0\} is considered. A regularization method for a solution of this problem with approximate data is proposed, and the convergence of this method for the class of functions that are analytic with respect to space variables is stated.