عنوان

Elliptic differential operators and spectral analysis /

(Number (ISBN

3030021254

(Number (ISBN

9783030021252

Erroneous ISBN

3030021246

Erroneous ISBN

9783030021245

Title Proper

Elliptic differential operators and spectral analysis /

General Material Designation

[Book]

First Statement of Responsibility

David E. Edmunds, W. Desmond Evans.

Place of Publication, Distribution, etc.

Cham :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

2018.

Specific Material Designation and Extent of Item

1 online resource

Series Title

Springer monographs in mathematics

Text of Note

Includes bibliographical references and index.

Text of Note

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

Text of Note

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

Text of Note

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

Text of Note

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

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Text of Note

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.--

Source for Acquisition/Subscription Address

Springer Nature

Stock Number

com.springer.onix.9783030021252

Title

Elliptic differential operators and spectral analysis.

International Standard Book Number

9783030021245

Differential equations, Elliptic.

Differential operators.

Functional Analysis.

Operator Theory.

Ordinary Differential Equations.

Partial Differential Equations.

Differential calculus & equations.

Differential equations, Elliptic.

Differential operators.

Functional analysis & transforms.

MATHEMATICS-- Calculus.

MATHEMATICS-- Mathematical Analysis.

MAT-- 005000

MAT-- 034000

PBKJ

PBKJ

Number

Edition

Class number

Edmunds, D. E., (David Eric)

Evans, W. D.

Date of Transaction

20200823073831.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y