Calculus of Variations and Nonlinear Partial Differential Equations
Title | Calculus of Variations and Nonlinear Partial Differential Equations PDF eBook |
Author | Luigi Ambrosio |
Publisher | Springer Science & Business Media |
Total Pages | 213 |
Release | 2008-01-02 |
Genre | Mathematics |
ISBN | 3540759131 |
With a historical overview by Elvira Mascolo
Calculus of Variations and Nonlinear Partial Differential Equations
Title | Calculus of Variations and Nonlinear Partial Differential Equations PDF eBook |
Author | Luigi Ambrosio |
Publisher | Springer |
Total Pages | 206 |
Release | 2007-12-03 |
Genre | Mathematics |
ISBN | 9783540759133 |
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
Title | Variational Methods PDF eBook |
Author | Michael Struwe |
Publisher | Springer Science & Business Media |
Total Pages | 288 |
Release | 2013-04-17 |
Genre | Science |
ISBN | 3662032120 |
Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radò. The book gives a concise introduction to variational methods and presents an overview of areas of current research in this field. This new edition has been substantially enlarged, a new chapter on the Yamabe problem has been added and the references have been updated. All topics are illustrated by carefully chosen examples, representing the current state of the art in their field.
Calculus of Variations and Partial Differential Equations
Title | Calculus of Variations and Partial Differential Equations PDF eBook |
Author | Luigi Ambrosio |
Publisher | Springer Science & Business Media |
Total Pages | 347 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3642571867 |
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
Title | Numerical Methods for Nonlinear Partial Differential Equations PDF eBook |
Author | Sören Bartels |
Publisher | Springer |
Total Pages | 394 |
Release | 2015-01-19 |
Genre | Mathematics |
ISBN | 3319137972 |
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.
Partial Differential Equations and the Calculus of Variations
Title | Partial Differential Equations and the Calculus of Variations PDF eBook |
Author | COLOMBINI |
Publisher | Springer Science & Business Media |
Total Pages | 503 |
Release | 2013-11-11 |
Genre | Mathematics |
ISBN | 1461598311 |
The Italian school of Mathematical Analysis has long and glo rious traditions. In the last thirty years it owes very much to the scientific pre-eminence of Ennio De Giorgi, Professor of Mathemati cal Analysis at the Scuola Normale Superiore di Pisa. His fundamental theorems in Calculus of Variations, in Minimal Surfaces Theory, in Partial Differential Equations, in Axiomatic Set Theory as well as the fertility of his mind to discover both general mathematical structures and techniques which frame many different problems, and profound and meaningful examples which show the limits of a theory and give origin to new results and theories, makes him an absolute reference point for all Italian mathematicians, and a well-known and valued personage in the international mathematical world. We have been students of Ennio de Giorgi. Now, we are glad to present to him, together with all his collegues, friends and former students, these Essays of Mathematical Analysis written in his hon our on the occasion of his sixtieth birthday (February 8th, 1988), with our best wishes and our thanks for all he gave in the past and will give us in the future. We have added to the research papers of this book the text of a conversation with Ennio De Giorgi about the diffusion and the communication of science and, in particular, of Mathematics.
An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞
Title | An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ PDF eBook |
Author | Nikos Katzourakis |
Publisher | Springer |
Total Pages | 123 |
Release | 2014-11-26 |
Genre | Mathematics |
ISBN | 3319128299 |
The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using "integration-by-parts" in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE.