Geometry in Partial Differential Equations
Geometry in Partial Differential Equations

Author: Agostino Prastaro

Publisher: World Scientific

Published: 1994

Total Pages: 482

ISBN-13: 9789810214074

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This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.

Geometry In Partial Differential Equations
Geometry In Partial Differential Equations

Author: Themistocles M Rassias

Publisher: World Scientific

Published: 1994-01-17

Total Pages: 480

ISBN-13: 9814504130

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This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.

Differential Geometry: Partial Differential Equations on Manifolds
Differential Geometry: Partial Differential Equations on Manifolds

Author: Robert Everist Greene

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 585

ISBN-13: 082181494X

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The first of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 1 begins with a problem list by S.T. Yau, successor to his 1980 list ( Sem

Nonlinear partial differential equations in differential geometry
Nonlinear partial differential equations in differential geometry

Author: Robert Hardt

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 356

ISBN-13: 9780821804315

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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.

Geometry of PDEs and Mechanics
Geometry of PDEs and Mechanics

Author: Agostino Prastaro

Publisher: World Scientific

Published: 1996

Total Pages: 764

ISBN-13: 9789810225209

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This volume presents the theory of partial differential equations (PDEs) from a modern geometric point of view so that PDEs can be characterized by using either technique of differential geometry or algebraic geometry. This allows us to recognize the richness of the structure of PDEs. It presents, for the first time, a geometric theory of non-commutative (quantum) PDEs and gives a general application of this theory to quantum field theory and quantum supergravity.

Geometric Partial Differential Equations and Image Analysis
Geometric Partial Differential Equations and Image Analysis

Author: Guillermo Sapiro

Publisher: Cambridge University Press

Published: 2006-02-13

Total Pages: 391

ISBN-13: 1139936514

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This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. This research area brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. State-of-the-art practical results in a large number of real problems are achieved with the techniques described in this book. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. This book will be a useful resource for researchers and practitioners. It is intended to provide information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.

Partial Differential Equations for Geometric Design
Partial Differential Equations for Geometric Design

Author: Hassan Ugail

Publisher: Springer Science & Business Media

Published: 2011-08-24

Total Pages: 110

ISBN-13: 0857297848

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The subject of Partial Differential Equations (PDEs) which first emerged in the 18th century holds an exciting and special position in the applications relating to the mathematical modelling of physical phenomena. The subject of PDEs has been developed by major names in Applied Mathematics such as Euler, Legendre, Laplace and Fourier and has applications to each and every physical phenomenon known to us e.g. fluid flow, elasticity, electricity and magnetism, weather forecasting and financial modelling. This book introduces the recent developments of PDEs in the field of Geometric Design particularly for computer based design and analysis involving the geometry of physical objects. Starting from the basic theory through to the discussion of practical applications the book describes how PDEs can be used in the area of Computer Aided Design and Simulation Based Design. Extensive examples with real life applications of PDEs in the area of Geometric Design are discussed in the book.

Partial Differential Equations and Geometric Measure Theory
Partial Differential Equations and Geometric Measure Theory

Author: Alessio Figalli

Publisher: Springer

Published: 2018-05-23

Total Pages: 224

ISBN-13: 3319740423

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This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.

Nonlinear PDEs, Their Geometry, and Applications
Nonlinear PDEs, Their Geometry, and Applications

Author: Radosław A. Kycia

Publisher: Springer

Published: 2019-05-18

Total Pages: 279

ISBN-13: 3030170314

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This volume presents lectures given at the Summer School Wisła 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures in the first part of this volume were delivered by experts in nonlinear differential equations and their applications to physics. Original research articles from members of the school comprise the second part of this volume. Much of the latter half of the volume complements the methods expounded in the first half by illustrating additional applications of geometric theory of differential equations. Various subjects are covered, providing readers a glimpse of current research. Other topics covered include thermodynamics, meteorology, and the Monge–Ampère equations. Researchers interested in the applications of nonlinear differential equations to physics will find this volume particularly useful. A knowledge of differential geometry is recommended for the first portion of the book, as well as a familiarity with basic concepts in physics.