Partial Differential Equations - Jürgen Jost

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Résumé :
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....

Biographie:
J?rgen Jost is Codirector of the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany, an Honorary Professor at the Department of Mathematics and Computer Sciences at Leipzig University, and an External Faculty Member of the Santa Fe Institute for the Sciences of Complexity, New Mexico, USA. He is the author of a number of further Springer textbooks including Postmodern Analysis (1997, 2002, 2005), Compact Riemann Surfaces (1997, 2002, 2006), Partial Differential Equations (2002, 2007, 2013), Differentialgeometrie und Minimalfl?chen (1994, 2007, 2014, with J. Eschenburg), Dynamical Systems (2005), Mathematical Concepts (2015), as well as several research monographs, such as Geometry and Physics (2009), and many publications in scientific journals....

Sommaire:
J?rgen Jost studierte von 1975 bis 1980 Mathematik, Physik, Volkswirtschaftslehre und Philosophie an der Universit?t Bonn. Er promovierte 1980 in der Mathematik und wurde nach verschiedenen internationalen Forschungsaufenthalten 1984 als Professor f?r Mathematik an die Ruhruniversit?t Bochum und 1996 als Direktor an das neu zu gr?ndende Max-Planck-Institut f?r Mathematik in den Naturwissenschaften in Leipzig berufen. Er ist auch Honorarprofessor an der Universit?t Leipzig und externes Fakult?tsmitglied des Santa Fe Institute for the Sciences of Complexity in den USA. 1993 erhielt er den Gottfried-Wilhelm-Leibniz-Preis der DFG und 2010 einen Advanced Grant des European Research Council. Er ist Autor von mehr als 20 Forschungsmonographien und Lehrb?chern und von ?ber 400 wissenschaftlichen Fachpublikationen. In seinen Forschungen verbindet er eine Vielzahl von mathematischen Disziplinen und Methoden mit einer allgemeinen Theorie komplexer Systeme und vielf?ltigen Anwendungen in der mathematischen und theoretischen Biologie und Neurobiologie....

From the reviews:

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

From the reviews of the third edition:

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)