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. Audience: This monograph will be of interest to mathematicians whose work involves partial differential equations, functional analysis, operator theory and the mathematics of mechanics.
This monograph presents elliptic, parabolic and hyperbolic boundary value problems for systems of mixed orders (Douglis-Nirenberg systems). For these problems the `theorem on complete collection of isomorphisms' is proven. Several applications in elasticity and hydrodynamics are treated. The book requires familiarity with the elements of functional analysis, the theory of partial differential equations, and the theory of generalized functions. Audience: This work will be of interest to graduate students and research mathematicians involved in areas such as functional analysis, partial differential equations, operator theory, the mathematics of mechanics, elasticity and viscoelasticity.
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.