A Priori Estimates for Solutions of Monge-Ampere Equations PDF Download
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Author: Friedmar Schulz
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
Author: Friedmar Schulz
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
Author: Cristian E. Gutierrez
Publisher: Springer Science & Business Media
ISBN: 9780817641771
Category : Mathematics
Languages : en
Pages : 148
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Book Description
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.
Author: Nam Q. Le
Publisher: American Mathematical Society
ISBN: 1470474204
Category : Mathematics
Languages : en
Pages : 599
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Book Description
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.
Author: Sebastien Picard
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
"The regularity theory of the degenerate complex Monge-Ampère equation is studied. First, the equation is considered on a compact Kahler manifold without boundary. Accordingly, some background information on Kahler geometry is presented. Given a solution of the degenerate complex Monge-Ampère equation, it is shown that its oscillation and gradient can be bounded. The Laplacian of the solution is also estimated. There is a slight improvement from the literature on the conditions required in order to obtain the estimate on the Laplacian of the solution, however the estimates developed only hold in the case of manifolds with non-negative bisectional curvature. As an application, a Dirichlet problem in complex space is considered. The obtained estimates are used to show existence and uniqueness of pluri-subharmonic solutions to the degenerate complex Monge-Ampere equation in a domain in complex space." --
Author: Hans Lewy
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: Hans Lewy (matematico.)
Publisher:
ISBN:
Category :
Languages : en
Pages : 10
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Author: Cristian E. Gutierrez
Publisher: Springer Science & Business Media
ISBN: 1461201950
Category : Mathematics
Languages : en
Pages : 140
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Book Description
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.
Author: Robert Hardt
Publisher: American Mathematical Soc.
ISBN: 9780821886847
Category : Mathematics
Languages : en
Pages : 356
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Book Description
This book contains lecture notes of minicourses at the Regional Geometry Institute at Park City, Utah, in July 1992. Presented here are surveys of breaking developments in a number of areas of nonlinear partial differential equations in differential geometry. The authors of the articles are not only excellent expositors, but are also leaders in this field of research. All of the articles provide in-depth treatment of the topics and require few prerequisites and less background than current research articles.
Author: Vincent Guedj
Publisher:
ISBN: 9783037191675
Category :
Languages : en
Pages : 472
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Book Description
![A C_1hn2-estimate [C-estimate] for solutions of complex Monge Ampère equations PDF](https://books.google.com/books/content/images/frontcover/K9exXwAACAAJ?fife=w80-h100)
Author: Friedmar Schulz
Publisher:
ISBN:
Category :
Languages : de
Pages : 20
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Book Description
