Partial Differential Equations
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Beschreibung
This book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. 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. This book can be utilized for a one-year course on partial differential equations.
Autor*in
Jürgen Jost
Themen in »Partial Differential Equations«
Maximum PDE Partial Differential Equations Sobolev space calculus differential equation hyperbolic equation maximum principle partial differential equation wave equation
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From the reviews:
MATHEMATICAL REVIEWS
"..the composition of this book is somewhat classical. Indeed the author covers the main properties of the elliptic, parabolic and hyperbolic equations. But he always adds some interesting extensions or links between these chapters…this textbook is self-contained…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."
"The author covers the main properties of the elliptic parabolic and hyperbolic equations. But he always adds some interesting extensions or links between these chapters. … With an appendix on general results concerning Banach or Hilbert spaces, this textbook is self-contained. … 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." (Alain Brillard, Mathematical Reviews, 2003f)
"Jost’s book … focuses mainly on elliptic PDEs and gives a comprehensive overview of the modern theory of solving such equations. … There are extremely helpful summaries and a handful of exercises at the end of each of the 11 chapters; an appendix covers background functional analysis. … Throughout, Jost achieves an impeccable blend of motivation, orientation and analysis … . 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, Vol. 88 (512), 2004)
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