Elliptic Partial Differential Equations Volume 1 Fredholm Theory of Elliptic Problems in Unbounded Domains 1st Edition by Vitaly Volpert 3034605366 9783034605366

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ISBN 10: 3034605366

ISBN 13: 9783034605366

Author: Vitaly Volpert

 

The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics. This monograph undertakes a systematic presentation of the theory of general elliptic operators. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators. Particular attention is paid to elliptic problems in unbounded domains which have not yet been sufficiently treated in the literature and which require some special approaches. The book also contains an analysis of non-Fredholm operators and discrete operators as well as extensive historical and bibliographical comments

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The selected topics and the author’s level of discourse will make this book a most useful resource for researchers and graduate students working in the broad field of partial differential equations and applications.

Elliptic Partial Differential Equations Volume 1 Fredholm Theory of Elliptic Problems in Unbounded Domains 1st Table of contents:

Chapter 1 Introduction

Chapter 2 Function Spaces and Operators

Chapter 3 A Priori Estimates

Chapter 4 Normal Solvability

Chapter 5 Fredholm Property

Chapter 6 Formally Adjoint Problems

Chapter 7 Elliptic Problems with a Parameter

Chapter 8 Index of Elliptic Operators

Chapter 9 Problems in Cylinders

Chapter 10 Non-Fredholm Operators

Chapter 11 Nonlinear Fredholm Operators

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