Analysis of a system of electrodynamic integro-differential equations with constant medium parameters. (Q1395220)

In this paper the properties of the operator \[ D(M)=-(\nabla\text{div}+k^2)\int\limits_{\Omega}M(y)\exp(ik|{x-y}|) /(4{\pi}|{x-y}|)\,dy, \qquad x\in{\Omega}\subset\mathbb R^3 \] in the space \(\mathbb L_2(\Omega)\) of complex-value vector functions are examined. The properties analyzed are used to prove a theorem on the smoothness of solutions to the system in terms of Sobolev spaces. 13 references are listed.