The Monge-Ampére equation and its applications
By: Alessio Figalli
Series: Zurich Lectures in Advanced Mathematics; Zurich lectures in advanced mathematics
Publisher: European Mathematical Society
Published: 2017
Place of publication: Zürich, Switzerland
Language: eng
Number of pages: 200
ISBN-13: 9783037191705
Subjects: Monge-Ampère equations; Partial Differential equations; Differential Geometry; Mathematical physics
Description: The Monge-Ampère equation is one of the most important partial differential equations, appearing in many problems in analysis and geometry. This monograph is a comprehensive introduction to the existence and regularity theory of the Monge-Ampère equation and some selected applications; the main goal is to provide the reader with a wealth of results and techniques he or she can draw from to understand current research related to this beautiful equation. The presentation is essentially self-contained, with an appendix wherein one can find precise statements of all the results used from different areas (linear algebra, convex geometry, measure theory, nonlinear analysis, and PDEs). This book is intended for graduate students and researchers interested in nonlinear PDEs: explanatory figures, detailed proofs, and heuristic arguments make this book suitable for self-study and also as a reference.
Notes: Includes bibliographical references (p. [191]-198) and index.