Spectral methods in surface superconductivity
Author(s)
Bibliographic Information
Spectral methods in surface superconductivity
（Progress in nonlinear differential equations and their applications / editor, Haim Brezis, v. 77）
Birkhäuser, c2010
- : hbk
Available at / 20 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hbkFOU||13||1200021326405
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Note
Includes bibliographical references
Description and Table of Contents
Description
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.
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.
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