Elliptic Differential Operators and Spectral Analysis
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Beschreibung
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.
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.
Presents core material on elliptic operators as well as advanced topics Provides detailed information about the function spaces related to elliptic operators Includes results on extensions of adjoint operators and applications to elliptic boundary value problems
Autor*in
D. E. Edmunds
Themen in »Elliptic Differential Operators and Spectral Analysis«
Elliptic operators self-adjoint extensions Sobolev spaces p-Laplacian spectral theory Schauder estimates regularity theory Dirac operator partial differential equations ordinary differential equations
Stimmen zu »Elliptic Differential Operators and Spectral Analysis«
“The book is well-written … . The presentation is self-contained and unified. … The book will be of interest to graduate students and to all researchers in PDEs.” (Petar Popivanov, zbMATH 1436.35003, 2020)
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