The Monge—Ampère Equation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Monge—Ampère Equation write by Cristian E. Gutierrez. This book was released on 2001-05-11. The Monge—Ampère Equation available in PDF, EPUB and Kindle. The Monge-Ampère equation has attracted considerable interest in recent years because of its important role in several areas of applied mathematics. Monge-Ampère type equations have applications in the areas of differential geometry, the calculus of variations, and several optimization problems, such as the Monge-Kantorovitch mass transfer problem. This book stresses the geometric aspects of this beautiful theory, using techniques from harmonic analysis – covering lemmas and set decompositions.
The Monge-Ampère Equation and Its Applications
The Monge-Ampère Equation and Its Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Monge-Ampère Equation and Its Applications write by Alessio Figalli. This book was released on 2017. The Monge-Ampère Equation and Its Applications available in PDF, EPUB and Kindle. The Monge-Ampere 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-Ampere 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 that contains 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.
The Monge—Ampère Equation
The Monge—Ampère Equation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Monge—Ampère Equation write by Cristian E. Gutierrez. This book was released on 2012-12-06. The Monge—Ampère Equation available in PDF, EPUB and Kindle. The Monge-Ampère equation has attracted considerable interest in recent years because of its important role in several areas of applied mathematics. Monge-Ampère type equations have applications in the areas of differential geometry, the calculus of variations, and several optimization problems, such as the Monge-Kantorovitch mass transfer problem. This book stresses the geometric aspects of this beautiful theory, using techniques from harmonic analysis – covering lemmas and set decompositions.
Nonlinear Analysis on Manifolds. Monge-Ampère Equations
Nonlinear Analysis on Manifolds. Monge-Ampère Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Analysis on Manifolds. Monge-Ampère Equations write by Thierry Aubin. This book was released on 2012-12-06. Nonlinear Analysis on Manifolds. Monge-Ampère Equations available in PDF, EPUB and Kindle. This volume is intended to allow mathematicians and physicists, especially analysts, to learn about nonlinear problems which arise in Riemannian Geometry. Analysis on Riemannian manifolds is a field currently undergoing great development. More and more, analysis proves to be a very powerful means for solving geometrical problems. Conversely, geometry may help us to solve certain problems in analysis. There are several reasons why the topic is difficult and interesting. It is very large and almost unexplored. On the other hand, geometric problems often lead to limiting cases of known problems in analysis, sometimes there is even more than one approach, and the already existing theoretical studies are inadequate to solve them. Each problem has its own particular difficulties. Nevertheless there exist some standard methods which are useful and which we must know to apply them. One should not forget that our problems are motivated by geometry, and that a geometrical argument may simplify the problem under investigation. Examples of this kind are still too rare. This work is neither a systematic study of a mathematical field nor the presentation of a lot of theoretical knowledge. On the contrary, I do my best to limit the text to the essential knowledge. I define as few concepts as possible and give only basic theorems which are useful for our topic. But I hope that the reader will find this sufficient to solve other geometrical problems by analysis.
Analysis of Monge–Ampère Equations
Analysis of Monge–Ampère Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analysis of Monge–Ampère Equations write by Nam Q. Le. This book was released on 2024-03-07. Analysis of Monge–Ampère Equations available in PDF, EPUB and Kindle. This book presents a systematic analysis of the Monge–Ampère equation, the linearized Monge–Ampère equation, and their applications, with emphasis on both interior and boundary theories. Starting from scratch, it gives an extensive survey of fundamental results, essential techniques, and intriguing phenomena in the solvability, geometry, and regularity of Monge–Ampère equations. It describes in depth diverse applications arising in geometry, fluid mechanics, meteorology, economics, and the calculus of variations. The modern treatment of boundary behaviors of solutions to Monge–Ampère equations, a very important topic of the theory, is thoroughly discussed. The book synthesizes many important recent advances, including Savin's boundary localization theorem, spectral theory, and interior and boundary regularity in Sobolev and Hölder spaces with optimal assumptions. It highlights geometric aspects of the theory and connections with adjacent research areas. This self-contained book provides the necessary background and techniques in convex geometry, real analysis, and partial differential equations, presents detailed proofs of all theorems, explains subtle constructions, and includes well over a hundred exercises. It can serve as an accessible text for graduate students as well as researchers interested in this subject.
