Elliptic differential operators and spectral analysis /

Elliptic differential operators and spectral analysis /

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Bibliographic Details
Author / Creator:Edmunds, D. E. (David Eric), author.
Imprint:Cham : Springer, 2018.
Description:1 online resource
Language:English
Series:Springer monographs in mathematics
Springer monographs in mathematics.
Subject:
Differential equations, Elliptic.
Differential operators.
Differential equations, Elliptic.
Differential operators.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11737641
Hidden Bibliographic Details
Other authors / contributors:Evans, W. D., author.
ISBN:9783030021252
3030021254
9783030021245
3030021246
Digital file characteristics:text file PDF
Notes:Includes bibliographical references and index.
Online resource; title from PDF title page (EBSCO, viewed November 27, 2018)
Summary:This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature. Starting with the basics of elliptic operators and their naturally associated function spaces, the authors then proceed to cover various related topics of current and continuing importance. Particular attention is given to the characterisation of self-adjoint extensions of symmetric operators acting in a Hilbert space and, for elliptic operators, the realisation of such extensions in terms of boundary conditions. A good deal of material not previously available in book form, such as the treatment of the Schauder estimates, is included. Requiring only basic knowledge of measure theory and functional analysis, the book is accessible to graduate students and will be of interest to all researchers in partial differential equations. The reader will value its self-contained, thorough and unified presentation of the modern theory of elliptic operators.--
Other form:Print version: Edmunds, D.E. (David Eric). Elliptic differential operators and spectral analysis. Cham : Springer, 2018 3030021246 9783030021245
Standard no.:10.1007/978-3-030-02125-2
Table of Contents:
  • Intro; Preface; Contents; Basic Notation; 1 Preliminaries; 1.1 Integration; 1.2 Functional Analysis; 1.3 Function Spaces; 1.3.1 Spaces of Continuous Functions; 1.3.2 Sobolev Spaces; 1.4 The Hilbert and Riesz Transforms; 2 The Laplace Operator; 2.1 Mean Value Inequalities; 2.2 Representation of Solutions; 2.3 Dirichlet Problems: The Method of Perron; 2.4 Notes; 3 Second-Order Elliptic Equations; 3.1 Basic Notions; 3.2 Maximum Principles; 4 The Classical Dirichlet Problem for Second-Order Elliptic Operators; 4.1 Preamble; 4.2 The Poisson Equation; 4.3 More General Elliptic Operators; 4.4 Notes
  • 5 Elliptic Operators of Arbitrary Order5.1 Preliminaries; 5.2 Gårding's Inequality; 5.3 The Dirichlet Problem; 5.4 A Little Regularity Theory; 5.5 Eigenvalues of the Laplacian; 5.6 Spectral Independence; 5.7 Notes; 6 Operators and Quadratic Forms in Hilbert Space; 6.1 Self-Adjoint Extensions of Symmetric Operators; 6.2 Characterisations of Self-Adjoint Extensions; 6.2.1 Linear Relations; 6.2.2 Boundary Triplets; 6.2.3 Gamma Fields and Weyl Functions; 6.3 The Friedrichs Extension; 6.4 The Krein-Vishik-Birman (KVB) Theory; 6.5 Adjoint Pairs and Closed Extensions; 6.6 Sectorial Operators
  • 7.3.3 Limit-Point and Limit-Circle Criteria7.4 Coercive Sectorial Operators; 7.4.1 The Case dim(kerT*) =2.; 7.5 Realisations of Second-Order Elliptic Operators on Domains; 7.6 Notes; 8 The Lp Approach to the Laplace Operator; 8.1 Preamble; 8.2 Technical Results; 8.3 Existence of a Weak Lp Solution; 8.4 Other Procedures; 8.5 Notes; 9 The p-Laplacian; 9.1 Preamble; 9.2 Preliminaries; 9.3 The Dirichlet Problem; 9.4 An Eigenvalue Problem; 9.5 More About the First Eigenvalue; 9.6 Notes; 10 The Rellich Inequality; 10.1 Preamble; 10.2 The Mean Distance Function
  • 10.3 Results Involving the Laplace Operator10.4 The p-Laplacian; 11 More Properties of Sobolev Embeddings; 11.1 The Distance Function; 11.2 Nuclear Maps; 11.3 Asymptotic Formulae for Approximation Numbers of Sobolev Embeddings; 11.4 Spaces with Variable Exponent; 11.5 Notes; 12 The Dirac Operator; 12.1 Preamble; 12.2 The Dirac Equation; 12.3 The Free Dirac Operator; 12.4 The Brown-Ravenhall Operator; 12.5 Sums of Operators and Coulomb Potentials; 12.5.1 The Case A= mathbbD; 12.5.2 The Case A = mathbbH; 12.5.3 The Case A= mathbbB; 12.6 The Free Dirac Operator on a Bounded Domain

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