Taylor - Partial Differential Equations III 2ed Sp

文件名称: Taylor - Partial Differential Equations III 2ed Springer 2011.pdf.pdf

所属分类: 专业指导

开发工具:

文件大小: 3mb

下载次数: 0

上传时间: 2019-07-22

提供者: eterna******

下载 (3mb)

不能下载？报告错误

详细说明：数学Taylor - Partial Differential Equations III 2ed Springer 2011 Taylor - Partial Differential Equations III 2ed Springer 2011 Michael E. Taylor Partial differential Equations ll Nonlinear equations Second edition ②$p ringer Michael E. Taylor Department of Mathematics University of North Carolina Chapel Hill, NC 27599 USA met math. unc. edu ISSN0066-5452 ISBN978-1-44197048-0 e-ISBN978-1-4419-7049-7 DOI10.1007/978-1-44197049-7 Springer New York dordrecht Heidelberg London Library of Congress Control Number: 2010937758 Mathematics Subject Classification(2010): 35AO1, 35A02, 35J05, 35J25, 35K05, 35L05, 35Q30 35Q35,35S05 C Springer Science+Business Media, LLC 1996, 201 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher(Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights Printed on acid-free paper SPringerispartofSpringerScience+businessMedia(www.springer.com) To my wife and daughter, Jane hawkins and Diane taylor Contents Contents of Volumes i and II Preface 13 Function Space and operator Theory for Nonlinear analysis 1 LP-Sobolev spaces 2 Sobolev imbedding theorems 3 Gagliardo-Nirenberg-Moser estimates.............. 8 4 Trudinger's inequalities 14 5 Singular integral operators on Lp.................. 17 he spaces H s,p 24 7 LP-Spectral theory of the Laplace operator 31 8 HOlder spaces and Zygmund spaces 40 9 Pseudodifferential operators with nonregular symbols...... 50 10 Paradifferential operators .60 11 Young measures and fuzzy functions 74 12 Hardy spaces.............................86 a Variations on complex interpolation 96 References 102 14 Nonlinear Elliptic Equations…....…...…….,105 1 A class of semilinear equations 107 2 Surfaces with negative curvature..................119 3 Local solvability of nonlinear elliptic equations 127 4 Elliptic regularity I (interior estimates) 135 5 Isometric imbedding of Riemannian manifolds.......... 147 6 Minimal surfaces 152 6b Second variation of area 168 7 The minimal surface equation ,176 8 Elliptic regularity II(boundary 185 9 Elliptic regularity III (De Giorgi-Nash-Moser theory)...... 196 10 The Dirichlet problem for quasi-linear elliptic equations 11 Direct methods in the calculus of variations 2 12 Quasi-linear elliptic systems 229 12B Further results on quasi-linear systems 244 13 Elliptic regularity Iv(Krylov-Safonov estimates) 58 viii contents 14 Regularity for a class of completely nonlinear equations...... 273 15 Monge-Ampere equations 16 Elliptic equations in two variables ····· 294 a Morrey spac ces 299 b Leray-Schauder fixed-point theorems ............... 302 References . .........................................................304 15 Nonlinear Parabolic equations 313 1 Semilinear parabolic equations................... 314 2 Applications to harmonic maps 325 3 Semilinear equations on regions with boundary 332 4 Reaction-diffusion equations. .................... 335 5 A nonlinear Trotter product formula................ 353 6 The Stefan problem 362 7 Quasi-linear parabolic equations I 376 8 Quasi-linear parabolic equations Il( sharper estimates 387 9 Quasi-linear parabolic equations III(Nash-Moser estimates).. 396 References 407 16 Nonlinear Hyperbolic Equations 413 1 Quasi-linear, symmetric hyperbolic systems. ......................414 2 Symmetrizable hyperbolic systems 425 3 Second-order and higher-order hyperbolic systems........ 432 4 Equations in the complex domain and the Cauchy Kowalewsky thed 445 5 Compressible fluid motion 448 6 Weak solutions to scalar conservation laws; the viscosity method 457 7 Systems of conservation laws in one space variable Riemann problems ····· 472 8 Entropy-flux pairs and riemann invariants 498 9 Global weak solutions of some 2 x 2 systems. ....................509 10 Vibrating strings revisited 517 References .524 17 Euler and Navier-Stokes Equations for Incompressible Fluids 1 Euler's equations for ideal incompressible fluid flow 532 2 Existence of solutions to the Euler equations. .....................54 3 Euler flows on bounded regions 553 4 Navier-Stokes equations . ..........................................561 5 Viscous flows on bounded regions 575 6 Vanishing viscosity limits..................... 586 7 From velocity field convergence to flow convergence...... 599 a Regularity for the Stokes system on bounded domains 605 References 610 Contents 18 Einsteins Equations............................615 I The gravitational field equations 616 Spherically symmetric spacetimes and the Schwarzschild solution 626 3 Stationary and static spacetimes 639 4 Orbits in Schwarzschild spacetime.…….649 5 Coupled Maxwell-Einstein equations............... 656 6 Relativistic fluids 7 Gravitational collapse ..670 8 The initial- value problen…………677 9 Geometry of initial surfaces..……………687 10 Time slices and their evolution 699 References 705 Index .711

(系统自动生成,下载前可以参看下载内容)