Boundary Value Problems in the Spaces of Distributions, 1999
Mathematics and Its Applications Series, Vol. 498

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.

0. Introduction.- 1. Green’s Formulas and Theorems on Complete Collection of Isomorphisms for General Elliptic Boundary Value Problems for Systems of Douglis—Nirenberg Structure.- 2. Elliptic Boundary Value Problems for General Systems of Equations with Additional Unknown Functions Defined at the Boundary of a Domain.- 3. Sobolev’s Problem.- 4. The Cauchy Problem for General Hyperbolic Systems in the Complete Scale of Sobolev Type Spaces.- 5. Boundary Value and Mixed Problems for General Hyperbolic Systems.- 6. Green’s Formula and Density of Solutions for General Parabolic Boundary Value Problems in Functional Spaces on Manifolds.- References.