Wave Factorization of Elliptic Symbols: Theory and Applications

This monograph is devoted to the development of a new approach to studying elliptic differential and integro-differential (pseudo-differential) equations and their boundary problems in non-smooth domains. This approach is based on a special representation of symbols of elliptic operators called wave factorization. In canonical domains, for example, the angle on a plane or a wedge in space, this yields a general solution, and then leads to the statement of a boundary problem. Wave factorization has also been used to obtain explicit formulas for solving some problems in diffraction and elasticity theory.