Regularity theory for quasilinear elliptic systems and Monge-Ampère equations in two dimensions / Friedmar Schulz

Auteur principal : Schulz, Friedmar, 1952-, AuteurType de document : Livre numériqueCollection : Lecture notes in mathematics, 1445Langue : anglais.Éditeur : Berlin : Springer-Verlag, 1990ISBN: 9783540531036.ISSN: 1617-9692.Sujet MSC : 35J60, PDEs - Elliptic equations and elliptic systems, Nonlinear elliptic equations
35B65, Qualitative properties of solutions to partial differential equations, Smoothness and regularity of solutions to PDEs
35J60, PDEs - Elliptic equations and elliptic systems, Nonlinear elliptic equations
53C42, Global differential geometry, Differential geometry of immersions
53C20, Global differential geometry, Global Riemannian geometry, including pinchingEn-ligne : Springerlink | Zentralblatt | MathSciNet
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The lecture notes presented here are an excellent introduction to the characteristic theory for two-dimensional Monge-Ampère equations. The presentation is self-contained and hence the auxiliary tools needed are also described. Included are excerpts from the regularity theory for elliptic systems, the theory of pseudoanalytic functions and the theory of conformal mappings with respect to a Riemannian metric, especially the connections between uniformization and second-order elliptic systems.
A great advantage of the book is that a number of important inequalities, useful also for related subjects, are given with detailed proofs. (MathSciNet)

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