The Monge-Ampère Equation

• Κύριος συγγραφέας: Gutiérrez, Cristian E. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.
• Έκδοση: 2nd ed. 2016.
• Σειρά: Progress in Nonlinear Differential Equations and Their Applications, 89
• Θέματα: Mathematics.; Partial differential equations.; Mathematical physics.; Differential geometry.; Partial Differential Equations.; Differential Geometry.; Mathematical Applications in the Physical Sciences.

Now in its second edition, this monograph explores the Monge-Ampère equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity results by L. A. Caffarelli. The geometric aspects...

Πίνακας περιεχομένων:

• Generalized Solutions to Monge-Ampère Equations
• Uniformly Elliptic Equations in Nondivergence Form
• The Cross-sections of Monge-Ampère
• Convex Solutions of detDu=1 in R<i>n
• Regularity Theory for the Monge-Ampère Equation
• W^2,p Estimates for the Monge-Ampère Equation
• The Linearized Monge-Ampère Equation
• Interior Hölder Estimates for Second Derivatives
• References
• Index.