Roitberg Y. Elliptic boundary value problems in the Spaces of Distributions

Kluwer Academic Publisher, 1996. — 432 p. — (Mathematics and its applications, v. 384). — ISBN: 0-7923-4303-4.This volume endeavours to summarise all available data on the theorems on isomorphisms and their ever increasing number of possible applications.
It deals with the theory of solvability in generalised functions of general boundary-value problems for elliptic equations. In the early sixties, 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.Functional spaces
Space H^s,p,(r)
Elliptic boundary-value problem
Theorem on comlete collection of isomorphisms
Elliptic problem with normal boundary condition
Traces of generalized solutions of elliptic equations on the boundary of the domain
Local Increase in the Smoothness of Generalized Solutions of Elliptic Boundry-Value Problems. Green’s Functions
Elliptic Problems with Power Singularities on the Right-Hand Sides. Degenerate Elliptic Problems
Elliptic Boundary-Value Problems with a Parameter
Elliptic Boundary-Value Problems for Systems of Equations