Mean Value Theorems and Properties of Solutions of Linear Differential Equations

Abstract

This paper describes an accompanying distributions technique that allows to obtain mean value formulas for linear homogeneous partial differential equations. One of these formulas can be interpreted as a generalization of the Asgeirsson principle for the string vibration equation into the case of an arbitrary natural order. In addition, this mean value formula is an exact difference scheme for a two-dimensional linear homogeneous equation with a symbol factorized up to linear factors.