Regularity Theory for Quasilinear Elliptic Systems and Monge - Ampere Equations in Two Dimensions

Friedmar Schulz (Autor)

Buch | Softcover

XVIII, 130 Seiten

1990 | 1990
Springer Berlin (Verlag)
978-3-540-53103-6 (ISBN)

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These lecture notes have been written as an introduction to the characteristic theory for two-dimensional Monge-Ampère equations, a theory largely developed by H. Lewy and E. Heinz which has never been presented in book form. An exposition of the Heinz-Lewy theory requires auxiliary material which can be found in various monographs, but which is presented here, in part because the focus is different, and also because these notes have an introductory character. Self-contained introductions to the regularity theory of elliptic systems, the theory of pseudoanalytic functions and the theory of conformal mappings are included. These notes grew out of a seminar given at the University of Kentucky in the fall of 1988 and are intended for graduate students and researchers interested in this area.

Prof. Dr. Friedmar Schulz war nach Studium, Promotion und Habilitation in Mathematik zunächst als Gastprofessor an verschiedenen Universitäten tätig, u.a. an der University of Minnesota, Minneapolis (USA); University of Iowa, Iowa City (USA); University of Kentucky, Lexington (USA); Australian National University, Canberra (Australien); University of Queensland, St. Lucia (Australien) und der Zhejiang University, Hangzhou (China). Seit 1994 ist er Professor für Mathematik mit Schwerpunkt Analysis und (Differential-)Geometrie an der Universität Ulm, wo er von 1995-1997 auch Dekan der Fakultät für Mathematik und Wirtschaftswissenschaften war. Seit 1998 ist er zudem außerordentlicher Professor der Changsha Railway University, Changsha, China. Professor Schulz ist Hauptherausgeber der im Oldenbourg Verlag erscheinenden Zeitschrift "Analysis. International mathematical journal of analysis and its applications".

Integral criteria for Hölder continuity.- Regularity for linear elliptic equations and quasilinear systems.- Regularity for Monge-Ampère equations.- Function theory of elliptic equations.- Univalent solutions of binary elliptic systems.- Conformal mappings with respect to a Riemannian metric.- Local behavior of solutions of differential inequalities.- Univalent solutions of Heinz-Lewy type systems.- A priori estimates for Monge-Ampère equations.- Regularity and a priori estimates for locally convex surfaces.

Erscheint lt. Verlag	24.10.1990
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XVIII, 130 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	234 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Elliptic systems • Elliptische Systeme • Equation • Function • Partial differential equations • Partielle Differentialgleichungen • Riemannian manifold
ISBN-10	3-540-53103-3 / 3540531033
ISBN-13	978-3-540-53103-6 / 9783540531036
Zustand	Neuware