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Elliptic Functional Differential Equations and Applications

  • Book
  • © 1997

Overview

Authors:
  1. Alexander L. Skubachevskii

    1. Moscow State Aviation Institute, Moscow, Russia

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Part of the book series: Operator Theory: Advances and Applications (OT, volume 91)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Alexander L. Skubachevskii
    Pages 1-17

  3. Boundary Value Problems for Functional Differential Equations in One Dimension

    • Alexander L. Skubachevskii
    Pages 19-89

  4. The First Boundary Value Problem for Strongly Elliptic Differential-Difference Equations

    • Alexander L. Skubachevskii
    Pages 91-159

  5. Applications to the Mechanics of a Deformable Body

    • Alexander L. Skubachevskii
    Pages 161-185

  6. Semi-Bounded Differential-Difference Operators with Degeneration

    • Alexander L. Skubachevskii
    Pages 187-209

  7. Nonlocal Elliptic Boundary Value Problems

    • Alexander L. Skubachevskii
    Pages 211-248

  8. Back Matter

    Pages 249-294
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Keywords

About this book

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.

Authors and Affiliations

  • Moscow State Aviation Institute, Moscow, Russia

    Alexander L. Skubachevskii

Bibliographic Information

  • Book Title: Elliptic Functional Differential Equations and Applications

  • Authors: Alexander L. Skubachevskii

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-9033-5

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 1997

  • Hardcover ISBN: 978-3-7643-5404-6Due: 18 February 1997

  • Softcover ISBN: 978-3-0348-9877-5Published: 01 October 2011

  • eBook ISBN: 978-3-0348-9033-5Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: X, 294

  • Topics: Analysis

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