Elliptic Boundary Value Problems in the Spaces of Distributions

Elliptic Boundary Value Problems in the Spaces of Distributions Synopsis

This volume attempts to summarize all available data on the theorems on isomorphisms and their ever increasing number of possible applications.;It deals with the theory of solvability in generalized functions of general boundary-value problems for elliptic equations. In the early 60s, Lions and Magenes, and Berezansky, Krein and Roitberg established the theorems on complete collection of isomorphisms. Further progress of the theory was connected with proving the theorem on complete collection of isomorphisms for new classes of problems, and hence with the development of new methods to prove these theorems. The theorems on isomorphisms were first established for elliptic equations with normal boundary conditions. However, after the Noetherian property of elliptic problems was proved without assuming the normality of the boundary expressions, this became the natural way to consider the problems of establishing the theorems on isomorphisms for general elliptic problems. The present author's method of solving this problem enabled proof of the theorem on complete collection of isomorphisms for the operators generated by elliptic boundary-value problems for general systems of equations.