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Calculus of Variations and Nonlinear Partial Differential Equations

2007-12-10 Mathematics
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Release : 2007-12-10
Genre : Mathematics
Kind : eBook
Book Rating : 14X/5 ( reviews)

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Book Synopsis Calculus of Variations and Nonlinear Partial Differential Equations by : Luigi Ambrosio

Download or read book Calculus of Variations and Nonlinear Partial Differential Equations written by Luigi Ambrosio. This book was released on 2007-12-10. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro, Italy in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. Coverage includes transport equations for nonsmooth vector fields, viscosity methods for the infinite Laplacian, and geometrical aspects of symmetrization.

Calculus of Variations and Nonlinear Partial Differential Equations

2007-12-03 Mathematics
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Release : 2007-12-03
Genre : Mathematics
Kind : eBook
Book Rating : 133/5 ( reviews)

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Book Synopsis Calculus of Variations and Nonlinear Partial Differential Equations by : Luigi Ambrosio

Download or read book Calculus of Variations and Nonlinear Partial Differential Equations written by Luigi Ambrosio. This book was released on 2007-12-03. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro, Italy in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. Coverage includes transport equations for nonsmooth vector fields, viscosity methods for the infinite Laplacian, and geometrical aspects of symmetrization.

Variational Methods

2013-04-17 Science
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Release : 2013-04-17
Genre : Science
Kind : eBook
Book Rating : 244/5 ( reviews)

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Book Synopsis Variational Methods by : Michael Struwe

Download or read book Variational Methods written by Michael Struwe. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: It would be hopeless to attempt to give a complete account of the history of the calculus of variations. The interest of Greek philosophers in isoperimetric problems underscores the importance of "optimal form" in ancient cultures, see Hildebrandt-Tromba [1] for a beautiful treatise of this subject. While variatio nal problems thus are part of our classical cultural heritage, the first modern treatment of a variational problem is attributed to Fermat (see Goldstine [1; p.l]). Postulating that light follows a path of least possible time, in 1662 Fer mat was able to derive the laws of refraction, thereby using methods which may already be termed analytic. With the development of the Calculus by Newton and Leibniz, the basis was laid for a more systematic development of the calculus of variations. The brothers Johann and Jakob Bernoulli and Johann's student Leonhard Euler, all from the city of Basel in Switzerland, were to become the "founding fathers" (Hildebrandt-Tromba [1; p.21]) of this new discipline. In 1743 Euler [1] sub mitted "A method for finding curves enjoying certain maximum or minimum properties", published 1744, the first textbook on the calculus of variations.

Calculus of Variations and Partial Differential Equations

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 867/5 ( reviews)

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Book Synopsis Calculus of Variations and Partial Differential Equations by : Luigi Ambrosio

Download or read book Calculus of Variations and Partial Differential Equations written by Luigi Ambrosio. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.

Numerical Methods for Nonlinear Partial Differential Equations

2015-01-19 Mathematics
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Release : 2015-01-19
Genre : Mathematics
Kind : eBook
Book Rating : 972/5 ( reviews)

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Book Synopsis Numerical Methods for Nonlinear Partial Differential Equations by : Sören Bartels

Download or read book Numerical Methods for Nonlinear Partial Differential Equations written by Sören Bartels. This book was released on 2015-01-19. Available in PDF, EPUB and Kindle. Book excerpt: The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

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