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Author : Gianni Dal Maso
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461203278
Author : Gianni Dal Maso
Publisher : Unknown
Page : 340 pages
File Size : 46,8 Mb
Release : 1993-01-01
Category : Calculus of variations
ISBN : 376433679X
Author : Andrea Braides
Publisher : Clarendon Press
Page : 230 pages
File Size : 40,7 Mb
Release : 2002-07-25
Category : Mathematics
ISBN : 9780191523199
The theory of Gamma-convergence is commonly recognized as an ideal and flexible tool for the description of the asymptotic behaviour of variational problems. Its applications range from the mathematical analysis of composites to the theory of phase transitions, from Image Processing to Fracture Mechanics. This text, written by an expert in the field, provides a brief and simple introduction to this subject, based on the treatment of a series of fundamental problems that illustrate the main features and techniques of Gamma-convergence and at the same time provide a stimulating starting point for further studies. The main part is set in a one-dimensional framework that highlights the main issues of Gamma-convergence without the burden of higher-dimensional technicalities. The text deals in sequence with increasingly complex problems, first treating integral functionals, then homogenisation, segmentation problems, phase transitions, free-discontinuity problems and their discrete and continuous approximation, making stimulating connections among those problems and with applications. The final part is devoted to an introduction to higher-dimensional problems, where more technical tools are usually needed, but the main techniques of Gamma-convergence illustrated in the previous section may be applied unchanged. The book and its structure originate from the author's experience in teaching courses on this subject to students at PhD level in all fields of Applied Analysis, and from the interaction with many specialists in Mechanics and Computer Vision, which have helped in making the text addressed also to a non-mathematical audience. The material of the book is almost self-contained, requiring only some basic notion of Measure Theory and Functional Analysis.
Author : Andrea Braides
Publisher : Springer
Page : 174 pages
File Size : 55,9 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9783319019826
This book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of notions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the definition of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions. The notions explored in the book are linked to existing findings for gradient flows, energetic solutions and local minimizers, for which some generalizations are also proposed.
Author : Andrea Braides
Publisher : Clarendon Press
Page : 238 pages
File Size : 50,8 Mb
Release : 2002
Category : Computers
ISBN : 0198507844
The point of the technique is to describe the asymptotic behavior of families of minimum problems. This textbook was developed from a lectures series for doctoral students in applied functional analysis to describe all the main features of the convergence to an audience primarily interested in applications but not intending to enter the specialty. Annotation copyrighted by Book News, Inc., Portland, OR
Author : Luigi Ambrosio,Norman Dancer
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642571862
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.
Author : Emil Artin
Publisher : Courier Dover Publications
Page : 48 pages
File Size : 41,5 Mb
Release : 2015-01-28
Category : Mathematics
ISBN : 9780486803005
This brief monograph on the gamma function was designed by the author to fill what he perceived as a gap in the literature of mathematics, which often treated the gamma function in a manner he described as both sketchy and overly complicated. Author Emil Artin, one of the twentieth century's leading mathematicians, wrote in his Preface to this book, "I feel that this monograph will help to show that the gamma function can be thought of as one of the elementary functions, and that all of its basic properties can be established using elementary methods of the calculus." Generations of teachers and students have benefitted from Artin's masterly arguments and precise results. Suitable for advanced undergraduates and graduate students of mathematics, his treatment examines functions, the Euler integrals and the Gauss formula, large values of x and the multiplication formula, the connection with sin x, applications to definite integrals, and other subjects.
Author : Walter G. Kropatsch,Nicole M. Artner,Ines Janusch
Publisher : Springer
Page : 400 pages
File Size : 40,5 Mb
Release : 2017-09-01
Category : Computers
ISBN : 9783319662725
This book constitutes the thoroughly refereed proceedings of the 20th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2017, held in Vienna, Austria, in September 2017. The 28 revised full papers presented together with 3 invited talks were carefully selected from 36 submissions. The papers are organized in topical sections on geometric transforms; discrete tomography; discrete modeling and visualization; morphological analysis; discrete shape representation, recognition and analysis; discrete and combinatorial topology; discrete models and tools; models for discrete geometry.
Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 206 pages
File Size : 54,9 Mb
Release : 2021-09-03
Category : Education
ISBN : 9781470466404
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Author : Michel Chipot
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 46,5 Mb
Release : 2009-03-29
Category : Mathematics
ISBN : 9783764399825
The aim of this book is to introduce the reader to different topics of the theory of elliptic partial differential equations by avoiding technicalities and refinements. Apart from the basic theory of equations in divergence form it includes subjects such as singular perturbation problems, homogenization, computations, asymptotic behaviour of problems in cylinders, elliptic systems, nonlinear problems, regularity theory, Navier-Stokes system, p-Laplace equation. Just a minimum on Sobolev spaces has been introduced, and work or integration on the boundary has been carefully avoided to keep the reader's attention on the beauty and variety of these issues. The chapters are relatively independent of each other and can be read or taught separately. Numerous results presented here are original and have not been published elsewhere. The book will be of interest to graduate students and faculty members specializing in partial differential equations.
Author : Michel Chipot,Pavol Quittner
Publisher : Elsevier
Page : 630 pages
File Size : 52,8 Mb
Release : 2006-08-08
Category : Mathematics
ISBN : 0080463827
This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Key features: - Written by well-known experts in the field - Self-contained volume in series covering one of the most rapid developing topics in mathematics - Written by well-known experts in the field - Self-contained volume in series covering one of the most rapid developing topics in mathematics
Author : Andrea Braides,Valeria Chiadò Piat
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 40,5 Mb
Release : 2006-11-22
Category : Mathematics
ISBN : 9783540365464
The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena is a challenging topic of very active research. This volume collects lecture notes on the asymptotic analysis of such problems when multi-scale behaviour derives from scale separation in the passage from atomistic systems to continuous functionals, from competition between bulk and surface energies, from various types of homogenization processes, and on concentration effects in Ginzburg-Landau energies and in subcritical growth problems.
Author : John Cagnol,Jean-Paul Zolesio
Publisher : CRC Press
Page : 306 pages
File Size : 50,6 Mb
Release : 2005-03-04
Category : Mathematics
ISBN : 1420027425
This volume comprises selected papers from the 21st Conference on System Modeling and Optimization in Sophia Antipolis, France. It covers over three decades of studies involving partial differential systems and equations. Topics include: the modeling of continuous mechanics involving fixed boundary, control theory, shape optimization and moving boundaries, and topological shape optimization. This edition discusses all developments that lead to current moving boundary analysis and the stochastic approach.
Author : Tomasz Komorowski,Claudio Landim,Stefano Olla
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 47,9 Mb
Release : 2012-07-05
Category : Mathematics
ISBN : 9783642298806
The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov processes, the book develops the techniques that allow us to deal with infinite dimensional models that appear in statistical mechanics and engineering (interacting particle systems, homogenization in random environments, and diffusion in turbulent flows, to mention just a few applications). The first part contains a detailed exposition of the method, and can be used as a text for graduate courses. The second concerns application to exclusion processes, in which the duality methods are fully exploited. The third part is about the homogenization of diffusions in random fields, including passive tracers in turbulent flows (including the superdiffusive behavior). There are no other books in the mathematical literature that deal with this kind of approach to the problem of the central limit theorem. Hence, this volume meets the demand for a monograph on this powerful approach, now widely used in many areas of probability and mathematical physics. The book also covers the connections with and application to hydrodynamic limits and homogenization theory, so besides probability researchers it will also be of interest also to mathematical physicists and analysts.
Author : Nikos Katzourakis
Publisher : Springer
Page : 123 pages
File Size : 52,5 Mb
Release : 2014-11-26
Category : Mathematics
ISBN : 9783319128290
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.