Boundary Value Problems in the Spaces of Distributions: 498 (Mathematics and Its Applications, 498) - Hardcover

Roitberg, Y.

Hardcover

ISBN 10: 0792360257 ISBN 13: 9780792360254

Publisher: Kluwer Academic Publishers, 1999

Synopsis

The present monograph is devoted to the theory of the solvability in generalized functions of general boundary value problems of mathematieal physies. It is the eontinuation of the author's book [Rl], where elliptic boundary value problems have been studied in eomplete seales of spaees of generalized funetions. From the early sixties, in the works of Lions and Magenes [LiM] and Yu. Berezanskii, S. Krein and Va. Roitberg [BKR] the theorems on eomplete eolleetion of isomorphisms have been established. These theorems, roughly speaking, mean that the operator generated by an elliptie boundary value problem establishes an isomorphism between spaees of functions which 'have s derivatives' and spaees functions whieh 'have s - r derivatives' (here s is an arbitrary real number, r is the order of the elliptic problem). The dose results were also obtained by Seheehter [Sehe]. These results and some of their applieations are eontained in the book of Lions and Magenes [LiM2] (see also the survey of Magenes [MagD and Yu. Berezanskii [Ber]. Further progress in the theory under eonsideration was eonneeted, first, with the completion of the dass of elliptie problems for whieh the theorems on eomplete eolleetion of isomorphisms hold, and, henee, with the development of new methods of proving of these theorems, and, second, with the inerease of a number of applieations of the isomorphism theorems. In the author's monograph [RI] the last years' investigations on the isomorphism theorems and some of their applieations have been presented.

About this title

Synopsis

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. This book requires familiarity with the elements of functional analysis, the theory of partial differential equations, and the theory of generalized functions. 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.

Edition details

• Publisher: Kluwer Academic Publishers
• Publication date: 1999
• Language: English
• ISBN 10: 0792360257
• ISBN 13: 9780792360254
• Binding: Hardcover
• Number of pages: 296