Elliptic differential-difference equations with differently directed translations in half-spaces
A. B. Muravnik
Abstract
We study the Dirichlet problem in the half-space for elliptic differentialdifference equations with operators being the compositions of differential operators and translation operators acting on spatial variables, which are independent variables ranging in the entire real axis. These equations generalize essentially the classical elliptic partial differential equations and they arise in various applications of mathematical physics, which are characterized by nonlocal and (or) inhomogeneous properties of the process or medium. In theoretical terms, an interest in such equations is due to the fact that they relate the values of the unknown function to each other (and its derivatives) not at one point, but at different points, which makes many classical methods not applicable.