Jürgen Jost

eBook, PDF

Partial Differential Equations (eBook, PDF)

Beschreibung

This book offers an ideal introduction to the theory of partial differential equations. It focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical analysis schemes), parabolic equations, variational methods, and continuity methods. This book also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. It also explores connections between elliptic, parabolic, and hyperbolic equations as well as the connection with Brownian motion and semigroups.

This second edition features a new chapter on reaction-diffusion equations and systems. There is also new material on Neumann boundary value problems, Poincaré inequalities, expansions as well as a new proof of the Hölder regularity of solutions of the Poisson equation.

Technische Details

• Geräte: PC
• ohne Kopierschutz
• Größe: 3.53MB

Barrierefreiheit

• Text-to-Speech

Autor

Jürgen Jost is currently a codirector of the Max Planck Institute for Mathematics in the Sciences and an honorary professor of mathematics at the University of Leipzig.

Produktdetails

• Verlag: Springer US
• Seitenzahl: 356
• Erscheinungstermin: 30. April 2010
• Englisch
• ISBN-13: 9780387493190
• Artikelnr.: 43727799

Rezensionen

From the reviews of the second edition:

"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

"It is an expanded translation by the author of the German original. ... The range of methods is wide, covering integral kernels, maximum principles, variational principles, gradient descents, weak derivatives and Sobolev spaces. ... the proof are clear and pleasant, provided the reader has a good command in integration theory. ... This book is an interesting introduction to the multiple facets of partial differential equations -- especially to regularity theory -- for the reader who has already a good background in analysis." (Jean Van Schaftingen, Bulletin of the Belgian Mathematical Society, 2007)

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