The Monge-Ampère equation and its applications / Alessio Figalli.

Format:

Book

Author/Creator:

Figalli, Alessio, 1984- author.

Contributor:

Rosengarten Family Fund.

Series:

Zurich lectures in advanced mathematics

Language:

English

Subjects (All):

Monge-Ampère equations.

Differential equations, Partial.

Geometry, Differential.

Mathematical physics.

Physical Description:

x, 200 pages : illustrations ; 24 cm.

Place of Publication:

Zürich : European Mathematical Society, [2017]

Summary:

"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."-- Back cover.

Contents:

Introduction

Alexandrov solutions

Smooth solutions

Interior regularity of weak solutions

Further results and extensions.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund.

ISBN:

9783037191705

3037191708

OCLC:

968195089

Publisher Number:

99996459632