TY  - BOOK
AU  - Figalli,Alessio
AU  - Figalli,Alessio
TI  - The Monge-Ampère Equation and Its Applications
T2  - Zurich Lectures in Advanced Mathematics (ZLAM)
SN  - 9783037196700
PY  - 2017///
CY  - Zuerich, Switzerland
PB  - European Mathematical Society Publishing House
KW  - Differential equations
KW  - bicssc
KW  - Differential & Riemannian geometry
KW  - Partial differential equations
KW  - msc
KW  - Differential geometry
N1  - Restricted to subscribers
N2  - 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
UR  - https://doi.org/10.4171/170
UR  - http://www.ems-ph.org/img/books/figalli_mini.jpg
ER  -