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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Taylor, Michael E. Partial Differential Equations III. Dordrecht : Springer, ©2010 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Michael E Taylor |

ISBN: | 9781441970497 1441970495 |

OCLC Number: | 769057778 |

Description: | 1 online resource : v.: digital. |

Contents: | Partial Differential Equations III; 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; 4 Trudinger's inequalities; 5 Singular integral operators on Lp; 6 The spaces Hs, p; 7 Lp-spectral theory of the Laplace operator; 8 Hölder spaces and Zygmund spaces; 9 Pseudodifferential operators with nonregular symbols; 10 Paradifferential operators; 11 Young measures and fuzzy functions; 12 Hardy spaces; A Variations on complex interpolation; References. 14 Nonlinear Elliptic Equations1 A class of semilinear equations; 2 Surfaces with negative curvature; 3 Local solvability of nonlinear elliptic equations; 4 Elliptic regularity I (interior estimates); 5 Isometric imbedding of Riemannian manifolds; 6 Minimal surfaces; 6B Second variation of area; 7 The minimal surface equation; 8 Elliptic regularity II (boundary estimates); 9 Elliptic regularity III (DeGiorgi-Nash-Moser theory); 10 The Dirichlet problem for quasi-linear elliptic equations; 11 Direct methods in the calculus of variations; 12 Quasi-linear elliptic systems. 12B Further results on quasi-linear systems13 Elliptic regularity IV (Krylov-Safonov estimates); 14 Regularity for a class of completely nonlinear equations; 15 Monge-Ampere equations; 16 Elliptic equations in two variables; A Morrey spaces; B Leray-Schauder fixed-point theorems; References; 15 Nonlinear Parabolic Equations; 1 Semilinear parabolic equations; 2 Applications to harmonic maps; 3 Semilinear equations on regions with boundary; 4 Reaction-diffusion equations; 5 A nonlinear Trotter product formula; 6 The Stefan problem; 7 Quasi-linear parabolic equations I. 8 Quasi-linear parabolic equations II (sharper estimates)9 Quasi-linear parabolic equations III (Nash-Moser estimates); References; 16 Nonlinear Hyperbolic Equations; 1 Quasi-linear, symmetric hyperbolic systems; 2 Symmetrizable hyperbolic systems; 3 Second-order and higher-order hyperbolic systems; 4 Equations in the complex domain and the Cauchy-Kowalewsky theorem; 5 Compressible fluid motion; 6 Weak solutions to scalar conservation laws; the viscosity method; 7 Systems of conservation laws in one space variable; Riemann problems; 8 Entropy-flux pairs and Riemann invariants. 9 Global weak solutions of some 22 systems10 Vibrating strings revisited; References; 17 Euler and Navier-Stokes Equations for Incompressible Fluids; 1 Euler's equations for ideal incompressible fluid flow; 2 Existence of solutions to the Euler equations; 3 Euler flows on bounded regions; 4 Navier-Stokes equations; 5 Viscous flows on bounded regions; 6 Vanishing viscosity limits; 7 From velocity field convergence to flow convergence; A Regularity for the Stokes system on bounded domains; References; 18 Einstein's Equations; 1 The gravitational field equations. |

Series Title: | Applied mathematical sciences (Springer-Verlag New York Inc.), 117. |

Responsibility: | by Michael E. Taylor. |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

From the reviews:"These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted."(SIAM Review, June 1998)From the reviews of the second edition:"This substantial three-volume work is an upgraded version of the comprehensive qualitative analysis of partial differential equations presented in the earlier edition. ... Graduate students ... will find these three volumes to be not just a fine and rigorous treatment of the subject, but also a source of inspiration to apply their knowledge and ability to the solution of other challenging problems in the field of partial differential equations. ... an excellent text for all devotees of the charming and thought-provoking byways of higher mathematics." (Christian Constanda, The Mathematical Association of America, July, 2011) Read more...

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