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Author : Bo Guan
Publisher :
ISBN 13 :
Total Pages : 142 pages
Book Rating : 4.:/5 (271 download)
Download or read book Boundary Value Problems for Surfaces of Prescribed Gauss Curvature and Monge-Ampère Equations written by Bo Guan and published by . This book was released on 1992 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jerry L. Kazdan
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889022
Total Pages : 68 pages
Book Rating : 4.8/5 (89 download)
Download or read book Prescribing the Curvature of a Riemannian Manifold written by Jerry L. Kazdan and published by American Mathematical Soc.. This book was released on 1985-12-31 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes were the basis for a series of ten lectures given in January 1984 at Polytechnic Institute of New York under the sponsorship of the Conference Board of the Mathematical Sciences and the National Science Foundation. The lectures were aimed at mathematicians who knew either some differential geometry or partial differential equations, although others could understand the lectures. Author's Summary:Given a Riemannian Manifold $(M,g)$ one can compute the sectional, Ricci, and scalar curvatures. In other special circumstances one also has mean curvatures, holomorphic curvatures, etc. The inverse problem is, given a candidate for some curvature, to determine if there is some metric $g$ with that as its curvature. One may also restrict ones attention to a special class of metrics, such as Kahler or conformal metrics, or those coming from an embedding. These problems lead one to (try to) solve nonlinear partial differential equations. However, there may be topological or analytic obstructions to solving these equations. A discussion of these problems thus requires a balanced understanding between various existence and non-existence results. The intent of this volume is to give an up-to-date survey of these questions, including enough background, so that the current research literature is accessible to mathematicians who are not necessarily experts in PDE or differential geometry. The intended audience is mathematicians and graduate students who know either PDE or differential geometry at roughly the level of an intermediate graduate course.
Author : Ulrich Dierkes
Publisher : Springer
ISBN 13 :
Total Pages : 540 pages
Book Rating : 4.3/5 (91 download)
Download or read book Minimal Surfaces: Boundary value problems written by Ulrich Dierkes and published by Springer. This book was released on 1992 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David Gilbarg
Publisher : Springer Science & Business Media
ISBN 13 : 9783540411604
Total Pages : 544 pages
Book Rating : 4.4/5 (116 download)
Download or read book Elliptic Partial Differential Equations of Second Order written by David Gilbarg and published by Springer Science & Business Media. This book was released on 2001-01-12 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work aims to be of interest to those who have to work with differential equations and acts either as a reference or as a book to learn from. The authors have made the treatment self-contained.
Author : Nam Q. Le
Publisher : American Mathematical Society
ISBN 13 : 1470476258
Total Pages : 599 pages
Book Rating : 4.4/5 (74 download)
Download or read book Analysis of Monge–Ampère Equations written by Nam Q. Le and published by American Mathematical Society. This book was released on 2024-03-08 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Michael E. Taylor
Publisher : Springer Science & Business Media
ISBN 13 : 1441970495
Total Pages : 734 pages
Book Rating : 4.4/5 (419 download)
Download or read book Partial Differential Equations III written by Michael E. Taylor and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is aimed at graduate students in mathematics, and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis
Author : Joel Spruck
Publisher :
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.F/5 ( download)
Download or read book Infinite Boundary Value Problems for Surfaces of Constant Mean Curvature written by Joel Spruck and published by . This book was released on 1971 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John I. E. Urbas
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (217 download)
Download or read book The Equation of Prescribed Gauss Curvature Without Boundary Conditions written by John I. E. Urbas and published by . This book was released on 1983 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alekseĭ Vasilʹevich Pogorelov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821886618
Total Pages : 680 pages
Book Rating : 4.8/5 (866 download)
Download or read book Extrinsic Geometry of Convex Surfaces written by Alekseĭ Vasilʹevich Pogorelov and published by American Mathematical Soc.. This book was released on 1973 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : I︠U︡riĭ Dmitrievich Burago
Publisher : Springer Science & Business Media
ISBN 13 : 9783540533771
Total Pages : 272 pages
Book Rating : 4.5/5 (337 download)
Download or read book Geometry III written by I︠U︡riĭ Dmitrievich Burago and published by Springer Science & Business Media. This book was released on 1992-09-23 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A volume devoted to the extremely clear and intrinsically beautiful theory of two-dimensional surfaces in Euclidean spaces. The main focus is on the connection between the theory of embedded surfaces and two-dimensional Riemannian geometry, and the influence of properties of intrinsic metrics on the geometry of surfaces.
Author : Dante Kalise
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110543591
Total Pages : 209 pages
Book Rating : 4.1/5 (15 download)
Download or read book Hamilton-Jacobi-Bellman Equations written by Dante Kalise and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-08-06 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal feedback control arises in different areas such as aerospace engineering, chemical processing, resource economics, etc. In this context, the application of dynamic programming techniques leads to the solution of fully nonlinear Hamilton-Jacobi-Bellman equations. This book presents the state of the art in the numerical approximation of Hamilton-Jacobi-Bellman equations, including post-processing of Galerkin methods, high-order methods, boundary treatment in semi-Lagrangian schemes, reduced basis methods, comparison principles for viscosity solutions, max-plus methods, and the numerical approximation of Monge-Ampère equations. This book also features applications in the simulation of adaptive controllers and the control of nonlinear delay differential equations. Contents From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving Hamilton–Jacobi–Bellman equations Improving policies for Hamilton–Jacobi–Bellman equations by postprocessing Viability approach to simulation of an adaptive controller Galerkin approximations for the optimal control of nonlinear delay differential equations Efficient higher order time discretization schemes for Hamilton–Jacobi–Bellman equations based on diagonally implicit symplectic Runge–Kutta methods Numerical solution of the simple Monge–Ampere equation with nonconvex Dirichlet data on nonconvex domains On the notion of boundary conditions in comparison principles for viscosity solutions Boundary mesh refinement for semi-Lagrangian schemes A reduced basis method for the Hamilton–Jacobi–Bellman equation within the European Union Emission Trading Scheme
Author : J N Flavin
Publisher : CRC Press
ISBN 13 : 9780849385124
Total Pages : 390 pages
Book Rating : 4.3/5 (851 download)
Download or read book Qualitative Estimates For Partial Differential Equations written by J N Flavin and published by CRC Press. This book was released on 1995-11-08 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Qualitative Estimates For Partial Differential Equations: An Introduction describes an approach to the use of partial differential equations (PDEs) arising in the modelling of physical phenomena. It treats a wide range of differential inequality techniques applicable to problems arising in engineering and the natural sciences, including fluid and solid mechanics, physics, dynamics, biology, and chemistry. The book begins with an elementary discussion of the fundamental principles of differential inequality techniques for PDEs arising in the solution of physical problems, and then shows how these are used in research. Qualitative Estimates For Partial Differential Equations: An Introduction is an ideal book for students, professors, lecturers, and researchers who need a comprehensive introduction to qualitative methods for PDEs arising in engineering and the natural sciences.
Author : Ioannis Athanasopoulos
Publisher : Routledge
ISBN 13 : 1351447130
Total Pages : 372 pages
Book Rating : 4.3/5 (514 download)
Download or read book Free Boundary Problems written by Ioannis Athanasopoulos and published by Routledge. This book was released on 2019-11-11 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Free boundary problems arise in an enormous number of situations in nature and technology. They hold a strategic position in pure and applied sciences and thus have been the focus of considerable research over the last three decades. Free Boundary Problems: Theory and Applications presents the work and results of experts at the forefront of current research in mathematics, material sciences, chemical engineering, biology, and physics. It contains the plenary lectures and contributed papers of the 1997 International Interdisciplinary Congress proceedings held in Crete. The main topics addressed include free boundary problems in fluid and solid mechanics, combustion, the theory of filtration, and glaciology. Contributors also discuss material science modeling, recent mathematical developments, and numerical analysis advances within their presentations of more specific topics, such as singularities of interfaces, cusp cavitation and fracture, capillary fluid dynamics of film coating, dynamics of surface growth, phase transition kinetics, and phase field models. With the implications of free boundary problems so far reaching, it becomes important for researchers from all of these fields to stay abreast of new developments. Free Boundary Problems: Theory and Applications provides the opportunity to do just that, presenting recent advances from more than 50 researchers at the frontiers of science, mathematics, and technology.
Author : Ilya J. Bakelman
Publisher : Springer Science & Business Media
ISBN 13 : 3642698816
Total Pages : 524 pages
Book Rating : 4.6/5 (426 download)
Download or read book Convex Analysis and Nonlinear Geometric Elliptic Equations written by Ilya J. Bakelman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Investigations in modem nonlinear analysis rely on ideas, methods and prob lems from various fields of mathematics, mechanics, physics and other applied sciences. In the second half of the twentieth century many prominent, ex emplary problems in nonlinear analysis were subject to intensive study and examination. The united ideas and methods of differential geometry, topology, differential equations and functional analysis as well as other areas of research in mathematics were successfully applied towards the complete solution of com plex problems in nonlinear analysis. It is not possible to encompass in the scope of one book all concepts, ideas, methods and results related to nonlinear analysis. Therefore, we shall restrict ourselves in this monograph to nonlinear elliptic boundary value problems as well as global geometric problems. In order that we may examine these prob lems, we are provided with a fundamental vehicle: The theory of convex bodies and hypersurfaces. In this book we systematically present a series of centrally significant results obtained in the second half of the twentieth century up to the present time. Particular attention is given to profound interconnections between various divisions in nonlinear analysis. The theory of convex functions and bodies plays a crucial role because the ellipticity of differential equations is closely connected with the local and global convexity properties of their solutions. Therefore it is necessary to have a sufficiently large amount of material devoted to the theory of convex bodies and functions and their connections with partial differential equations.
Author : Rolf Schneider
Publisher : Cambridge University Press
ISBN 13 : 0521352207
Total Pages : 506 pages
Book Rating : 4.5/5 (213 download)
Download or read book Convex Bodies written by Rolf Schneider and published by Cambridge University Press. This book was released on 1993-02-25 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to convex bodies giving full proofs for some deeper theorems which have never previously been brought together.
Author : Cristian E. Gutierrez
Publisher : Springer Science & Business Media
ISBN 13 : 9780817641771
Total Pages : 148 pages
Book Rating : 4.6/5 (417 download)
Download or read book The Monge—Ampère Equation written by Cristian E. Gutierrez and published by Springer Science & Business Media. This book was released on 2001-05-11 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : John I. E. Urbas
Publisher :
ISBN 13 :
Total Pages : 33 pages
Book Rating : 4.:/5 (22 download)
Download or read book Boundary Regularity for Solutions of the Equation of Prescribed Gauss Curvature written by John I. E. Urbas and published by . This book was released on 1989 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
