Overview

During the past decade, the mathematics of superconductivity has been the subject of intense activity. This book examines in detail the nonlinear Ginzburg–Landau functional, the model most commonly used in the study of superconductivity. Specifically covered are cases in the presence of a strong magnetic field and with a sufficiently large Ginzburg–Landau parameter kappa. Spectral Methods in Surface Superconductivity is intended for students and researchers with a graduate-level understanding of functional analysis, spectral theory, and the analysis of partial differential equations. The book also includes an overview of all nonstandard material as well as important semi-classical techniques in spectral theory that are involved in the nonlinear study of superconductivity.

Full Product Details

Author:   Søren Fournais ,  Bernard Helffer
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Volume:   77
Dimensions:   Width: 15.50cm , Height: 2.00cm , Length: 23.50cm
Weight:   1.460kg
ISBN:  

9780817647964

ISBN 10:   0817647961
Pages:   324
Publication Date:   15 June 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table of Contents

Preface.- Notation.- Part I Linear Analysis.- 1 Spectral Analysis of Schrodinger Operators.- 2 Diamagnetism.- 3 Models in One Dimension.- 4 Constant Field Models in Dimension 2: Noncompact Case.- 5 Constant Field Models in Dimension 2: Discs and Their Complements.- 6 Models in Dimension 3: R3 or R3,+.- 7 Introduction to Semiclassical Methods for the Schrodinger Operator with a Large Electric Potential.- 8 Large Field Asymptotics of the Magnetic Schrodinger Operator: The Case of Dimension 2.- 9 Main Results for Large Magnetic Fields in Dimension 3.- Part II Nonlinear Analysis.-10 The Ginzburg-Landau Functional.- 11 Optimal Elliptic Estimates.- 12 Decay Estimates.- 13 On the Third Critical Field HC3.- 14 Between HC2 and HC3 in Two Dimensions.- 15 On the Problems with Corners.- 16 On Other Models in Superconductivity and Open Problems.- A Min-Max Principle.- B Essential Spectrum and Persson's Theorem.- C Analytic Perturbation Theory.- D About the Curl-Div System.- E Regularity Theorems and Precise Estimates in Elliptic PDE.- F Boundary Coordinates.- References.- Index.

Reviews

From the reviews: The book is concerned with the analysis of mathematical problems connected with the theory of superconductivity. The authors consider a standard basic model of superconductivity described by the Ginzburg-Landau functional. ! The authors attempt to make the book self-contained, having graduate students and researchers in mind. For this purpose, at the end of the book they add various appendices containing somewhat standard material. ! The book concludes with a fairly complete bibliography on the subject. (Yuri A. Kordyukov, Mathematical Reviews, Issue 2011 j)

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