Selected Works of Eberhard Hopf with Commentaries: With CommentariesThis work celebrates the work of Eberhard Hopf, a founding father of ergodic theory, a mathematician who produced many beautiful, elegantly written, and now classical, results in integral equations and partial differential equations. Hopf's results remain at the core of these fields, and the title includes Hopf's original mathematical papers, still notable for their elegance and clarity of the writing, with accompanying summaries and commentary by well-known mathematicians. Today, ergodic theory and P.D.E. continue to be active, important areas of mathematics. In this volume the reader will find the roots of many ergodic theory concepts and theorems. Hopf authored fundamental results for P.D.E., such as the maximum principle of elliptic equations and the complete solution of Burger's equation. The familiar properties of elliptic equations were proved for the first time in his earliest work and are included here. His bifurcation theorem, still used over and over again, is a particular gem. The proof of the Wiener-Hopf Theorem is a stunning application of deep analysis. The volume is presented in two main parts. The first section is dedicated to classical papers in analysis and fluid dynamics, and the second to ergodic theory. These works and all the others in the Selected Works carry commentaries by a stellar group of mathematicians who write of the origin of the problems, the important results that followed. Many a mathematical researcher and graduate student will find these collected works to be an excellent resource. |
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Contents
Commentary by James B Serrin | 9 |
A Remark on Linear Elliptic Differential Equations of Second Order | 15 |
Zum analytischen Charakter der Losungen regularer zweidimensionaler | 21 |
Commentary by Hans Weinberger | 31 |
Commentary by Harold Widom | 47 |
Losungen elliptischer Differentialgleichungen zweiter Ordnung | 49 |
Commentary by Hans Weinberger | 89 |
Commentary by Martin Golubitsky and Paul H Rabinowitz | 111 |
Commentaries by Roger Temam | 147 |
Commentary by Peter Lax | 189 |
Commentary by James B Serrin | 213 |
Commentary by Cathleen S Morawetz | 269 |
Statistik der Losungen geodatischer Probleme vom unstabilen Typus II | 317 |
Commentaries by Ya G Sinai | 337 |
On the Ergodic Theorem for Positive Linear Operators | 387 |
A mathematical example displaying features of turbulence | 127 |
Common terms and phrases
Ableitungen analytisch asymptotisch Bedingung Behauptung beiden beliebig Bereiche beschränkt Beweis beweisen bewiesen bifurcation boundary COMMENTARIES continuous function daher definiert differential equations differential inequality Differentialgleichungen EBERHARD HOPF Eigenschaften einmal elliptischen endlich erfüllt ergibt ergodic theory erste ersten Exponenten Feld Ferner festen fiir Flächen fluid Folge folgende folgenden folgt follows function Funktionen für Gebiete genügend genügt geodätische Strömung Geodätischen gibt gilt gleich gleichmäßig Gleichung Gleichungen Halbstrahlen Hamilton-Jacobi equation Hopf theorem Hopf's inequality initial value problem initial values Integral jedem Klasse Koeffizienten konst konstant längs leicht Lemma limit linear Linienelemente Lipschitz continuous Lösung Lösungen Maß Math maximum principle Menge muß Navier-Stokes equations Null obigen partial differential equations phase positiv problem proof Punkte Raum regulär Richtung satisfies Satz segment seien Sinne somit Stelle stetig differenzierbar theorem überall unendlich Ungleichung Voraussetzung weak solution wieder Winkel zunächst zwei zweiten zweiter Ordnung
Bibliographic information
| Title | Selected Works of Eberhard Hopf with Commentaries: With Commentaries Volume 17 of Collected works series: American Mathematical Society |
| Authors | Eberhard Hopf, Cathleen S. Morawetz, James Serrin |
| Editors | Cathleen S. Morawetz, James Serrin, Yakov G. Sinai |
| Edition | illustrated |
| Publisher | American Mathematical Soc., 2002 |
| ISBN | 082182077X, 9780821820773 |
| Length | 396 pages |
| Subjects | › Mathematics / Mathematical Analysis |
| Export Citation | BiBTeX EndNote RefMan |