Del 214 i serien Graduate Texts in Mathematics

Partial Differential Equations

Häftad, Engelska, 2014

AvJürgen Jost

929 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

Finns i fler format (2)

Häftad

859 kr

Skickas inom 10-15 vardagar

Inbunden

1 279 kr

Skickas inom 10-15 vardagar

This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these fundamental types. Aspects of Brownian motion or pattern formation processes are also presented. The second part focuses on existence schemes and develops estimates for solutions of elliptic equations, such as Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. In particular, the reader will learn the basic techniques underlying current research in elliptic partial differential equations. This revised and expanded third edition is enhanced with many additional examples that will help motivate the reader. New features include a reorganized and extended chapter on hyperbolic equations, as well as a new chapter on the relations between different types of partial differential equations, including first-order hyperbolic systems, Langevin and Fokker-Planck equations, viscosity solutions for elliptic PDEs, and much more. Also, the new edition contains additional material on systems of elliptic partial differential equations, and it explains in more detail how the Harnack inequality can be used for the regularity of solutions.

Produktinformation

Utgivningsdatum2014-12-13
Mått155 x 235 x 26 mm
Vikt640 g
FormatHäftad
SpråkEngelska
SerieGraduate Texts in Mathematics
Antal sidor410
Upplaga3
FörlagSpringer-Verlag New York Inc.
ISBN9781493902477

Tillhör följande kategorier

Preface.- Introduction: What are Partial Differential Equations?.- 1 The Laplace equation as the Prototype of an Elliptic Partial Differential Equation of Second Order.- 2 The Maximum Principle.- 3 Existence Techniques I: Methods Based on the Maximum Principle.- 4 Existence Techniques II: Parabolic Methods. The Heat Equation.- 5 Reaction-Diffusion Equations and Systems.- 6 Hyperbolic Equations.- 7 The Heat Equation, Semigroups, and Brownian Motion.- 8 Relationships between Different Partial Differential Equations.- 9 The Dirichlet Principle. Variational Methods for the Solutions of PDEs (Existence Techniques III).- 10 Sobolev Spaces and L^2 Regularity theory.- 11 Strong solutions.- 12 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV).- 13The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash.- Appendix: Banach and Hilbert spaces. The L^p-Spaces.- References.- Index of Notation.- Index.

From the book reviews: "This graduate-level book is an introduction to the modern theory of partial differential equations (PDEs) with an emphasis on elliptic PDEs. ... The book is undoubtedly a success in the presentation of diverse methods in PDEs at such an introductory level. The reader has a great opportunity to learn basic techniques underlying current research in elliptic PDEs and be motivated for advanced theory of more general elliptic PDEs and nonlinear PDEs." (Dhruba Adhikari, MAA Reviews, December, 2014) "This revised version gives an introduction to the theory of partial differential equations. ... Every chapter has at the end a very helpful summary and some exercises. This book is very useful for a PhD course." (Vincenzo Vespri, Zentralblatt MATH, Vol. 1259, 2013) "Because of the nice global presentation, I recommend this book to students and young researchers who need the now classical properties of these second-order partial differential equations. Teachers will also find in this textbook the basis of an introductory course on second-order partial differential equations." - Alain Brillard, Mathematical Reviews "Beautifully written and superbly well-organised, I strongly recommend this book to anyone seeking a stylish, balanced, up-to-date survey of this central area of mathematics." - Nick Lord, The Mathematical Gazette