Elliptic Functional Differential Equations and Applications (Operator Theory: Advances and Applications, 91) - Hardcover

Skubachevskii, Alexander L.

Hardcover

ISBN 10: 3764354046 ISBN 13: 9783764354046

Publisher: Birkhäuser, 1997

Synopsis

Boundary value problems for elliptic differential-difference equations have some astonishing properties. For example, unlike elliptic differential equations, the smoothness of the generalized solutions can be broken in a bounded domain and is preserved only in some subdomains. The symbol of a self-adjoint semibounded functional differential operator can change its sign. The purpose of this book is to present for the first time general results concerning solvability and spectrum of these problems, a priori estimates and smoothness of solutions. The approach is based on the properties of elliptic operators and difference operators in Sobolev spaces. The most important features distinguishing this work are applications to different fields of science. The methods in this book are used to obtain new results regarding the solvability of nonlocal elliptic boundary value problems and the existence of Feller semigroups for multidimensional diffusion processes. Moreover, applications to control theory and aircraft and rocket technology are given. The theory is illustrated with numerous figures and examples. The book is addresssed to graduate students and researchers in partial differential equations and functional differential equations. It will also be of use to engineers in control theory and elasticity theory.

Edition details

• Publisher: Birkhäuser
• Publication date: 1997
• ISBN 10: 3764354046
• ISBN 13: 9783764354046
• Binding: Hardcover
• Language: English
• Number of pages: 304