Free Discontinuity Problems

Author : Andrea Braides
Publisher : Springer
Page : 160 pages
File Size : 51,6 Mb
Release : 2006-11-13
Category : Mathematics
ISBN : 9783540687146

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Approximation of Free-Discontinuity Problems by Andrea Braides Pdf

Functionals involving both volume and surface energies have a number of applications ranging from Computer Vision to Fracture Mechanics. In order to tackle numerical and dynamical problems linked to such functionals many approximations by functionals defined on smooth functions have been proposed (using high-order singular perturbations, finite-difference or non-local energies, etc.) The purpose of this book is to present a global approach to these approximations using the theory of gamma-convergence and of special functions of bounded variation. The book is directed to PhD students and researchers in calculus of variations, interested in approximation problems with possible applications.

Author : Nicola Fusco,Aldo Pratelli
Publisher : Springer
Page : 237 pages
File Size : 50,5 Mb
Release : 2017-02-02
Category : Mathematics
ISBN : 9788876425936

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Free Discontinuity Problems by Nicola Fusco,Aldo Pratelli Pdf

This book presents a series of lectures on three of the best known examples of free discontinuity problems: the Mumford-Shah model for image segmentation, a variational model for the epitaxial growth of thin films, and the sharp interface limit of the Ohta-Kawasaki model for pattern formation in dyblock copolymers.

Author : Andrea Braides
Publisher : Unknown
Page : 148 pages
File Size : 44,7 Mb
Release : 1998
Category : Electronic
ISBN : OCLC:1136555690

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Approximation of Free-discontinuity Problems by Andrea Braides Pdf

Author : Guido De Philippis,Xavier Ros-Oton,Georg S. Weiss
Publisher : Springer Nature
Page : 138 pages
File Size : 48,8 Mb
Release : 2021-03-23
Category : Mathematics
ISBN : 9783030657994

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Geometric Measure Theory and Free Boundary Problems by Guido De Philippis,Xavier Ros-Oton,Georg S. Weiss Pdf

This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school “Geometric Measure Theory and Applications – From Geometric Analysis to Free Boundary Problems” which took place in Cetraro, Italy, under the scientific direction of Matteo Focardi and Emanuele Spadaro. Providing a description of the structure of measures satisfying certain differential constraints, and covering regularity theory for Bernoulli type free boundary problems and water waves as well as regularity theory for the obstacle problems and the developments leading to applications to the Stefan problem, this volume will be of interest to students and researchers in mathematical analysis and its applications.

Author : Pierluigi Colli,Angelo Favini,Elisabetta Rocca,Giulio Schimperna,Jürgen Sprekels
Publisher : Springer
Page : 571 pages
File Size : 46,6 Mb
Release : 2017-11-03
Category : Mathematics
ISBN : 9783319644899

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Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs by Pierluigi Colli,Angelo Favini,Elisabetta Rocca,Giulio Schimperna,Jürgen Sprekels Pdf

This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.

Author : Pierluigi Colli,Claudio Verdi,Augusto Visintin
Publisher : Birkhäuser
Page : 342 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878937

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Free Boundary Problems by Pierluigi Colli,Claudio Verdi,Augusto Visintin Pdf

Many phenomena of interest for applications are represented by differential equations which are defined in a domain whose boundary is a priori unknown, and is accordingly named a "free boundary". A further quantitative condition is then provided in order to exclude indeterminacy. Free boundary problems thus encompass a broad spectrum which is represented in this state-of-the-art volume by a variety of contributions of researchers in mathematics and applied fields like physics, biology and material sciences. Special emphasis has been reserved for mathematical modelling and for the formulation of new problems.

Author : Anonim
Publisher : ScholarlyEditions
Page : 995 pages
File Size : 52,9 Mb
Release : 2012-01-09
Category : Mathematics
ISBN : 9781464964794

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Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition by Anonim Pdf

Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Logic, Operations, and Computational Mathematics and Geometry. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Logic, Operations, and Computational Mathematics and Geometry in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Author : Gianni Dal Maso,Antonio de Simone,Franco Tomarelli
Publisher : Springer Science & Business Media
Page : 166 pages
File Size : 44,8 Mb
Release : 2006-06-23
Category : Technology & Engineering
ISBN : 9783764375652

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Variational Problems in Materials Science by Gianni Dal Maso,Antonio de Simone,Franco Tomarelli Pdf

This volume contains the proceedings of the international workshop Variational Problems in Materials Science. Coverage includes the study of BV vector fields, path functionals over Wasserstein spaces, variational approaches to quasi-static evolution, free-discontinuity problems with applications to fracture and plasticity, systems with hysteresis or with interfacial energies, evolution of interfaces, multi-scale analysis in ferromagnetism and ferroelectricity, and much more.

Author : Andrea Braides
Publisher : Clarendon Press
Page : 230 pages
File Size : 55,7 Mb
Release : 2002-07-25
Category : Mathematics
ISBN : 9780191523199

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Gamma-Convergence for Beginners by Andrea Braides Pdf

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 : Gianni Dal Maso,Franco Tomarelli
Publisher : Birkhäuser
Page : 195 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034881937

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Variational Methods for Discontinuous Structures by Gianni Dal Maso,Franco Tomarelli Pdf

This volume contains the Proceedings of the International Workshop Variational Methods For Discontinuous Structures, which was jointly organized by the Dipar timento di Matematica Francesco Brioschi of Milano Politecnico and the Interna tional School for Advanced Studies (SISSA) of Trieste. The Conference took place at Villa Erba Antica (Cernobbio) on the Lago di Como on July 4- 6, 2001. In past years the calculus of variations faced mainly the study of continuous structures, say particularly problems with smooth solutions. One of the deepest and more delicate problems was the regularity of weak solutions. More recently, new sophisticated tools have been introduced in order to study discontinuities: in many variational problems solutions develop singularities, and sometimes the most interesting part of a solution is the singularity itself. The conference intended to focus on recent developments in this direction. Some of the talks were devoted to differential or variational modelling of image segmentation, occlusion and textures synthesizing in image analysis, varia tional description of micro-magnetic materials, dimension reduction and structured deformations in elasticity and plasticity, phase transitions, irrigation and drainage, evolution of crystalline shapes; in most cases theoretical and numerical analysis of these models were provided. viii Preface Other talks were dedicated to specific problems of the calculus of variations: variational theory of weak or lower-dimensional structures, optimal transport prob lems with free Dirichlet regions, higher order variational problems, symmetrization in the BV framework.

Author : Luigi Ambrosio,Norman Dancer
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 49,6 Mb
Release : 2000-01-24
Category : Mathematics
ISBN : 3540648038

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Calculus of Variations and Partial Differential Equations by Luigi Ambrosio,Norman Dancer Pdf

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 : Antal Balog,D. Szasz,A. Recski,G.D.H. Katona
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 41,6 Mb
Release : 1998-07-21
Category : Mathematics
ISBN : 3764354976

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European Congress of Mathematics by Antal Balog,D. Szasz,A. Recski,G.D.H. Katona Pdf

This is the first volume of the procedings of the second European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners. Together with volume II it contains a collection of contributions by the invited lecturers. Finally, volume II also presents reports on some of the Round Table discussions. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: Vol. I: N. Alon, L. Ambrosio, K. Astala, R. Benedetti, Ch. Bessenrodt, F. Bethuel, P. Bjørstad, E. Bolthausen, J. Bricmont, A. Kupiainen, D. Burago, L. Caporaso, U. Dierkes, I. Dynnikov, L.H. Eliasson, W.T. Gowers, H. Hedenmalm, A. Huber, J. Kaczorowski, J. Kollár, D.O. Kramkov, A.N. Shiryaev, C. Lescop, R. März. Vol. II: J. Matousek, D. McDuff, A.S. Merkurjev, V. Milman, St. Müller, T. Nowicki, E. Olivieri, E. Scoppola, V.P. Platonov, J. Pöschel, L. Polterovich , L. Pyber, N. Simányi, J.P. Solovej, A. Stipsicz, G. Tardos, J.-P. Tignol, A.P. Veselov, E. Zuazua

Author : Michel Chipot,Pavol Quittner
Publisher : Elsevier
Page : 630 pages
File Size : 54,9 Mb
Release : 2006-08-08
Category : Mathematics
ISBN : 0080463827

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Handbook of Differential Equations: Stationary Partial Differential Equations by Michel Chipot,Pavol Quittner Pdf

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 : Raul Serapioni,Franco Tomarelli
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 49,8 Mb
Release : 1996-08-28
Category : Gardening
ISBN : 3764352736

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Variational Methods for Discontinuous Structures by Raul Serapioni,Franco Tomarelli Pdf

In recent years many researchers in material science have focused their attention on the study of composite materials, equilibrium of crystals and crack distribution in continua subject to loads. At the same time several new issues in computer vision and image processing have been studied in depth. The understanding of many of these problems has made significant progress thanks to new methods developed in calculus of variations, geometric measure theory and partial differential equations. In particular, new technical tools have been introduced and successfully applied. For example, in order to describe the geometrical complexity of unknown patterns, a new class of problems in calculus of variations has been introduced together with a suitable functional setting: the free-discontinuity problems and the special BV and BH functions. The conference held at Villa Olmo on Lake Como in September 1994 spawned successful discussion of these topics among mathematicians, experts in computer science and material scientists.

Author : Michel Fremond,Franco Maceri
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 48,6 Mb
Release : 2006-07-16
Category : Technology & Engineering
ISBN : 9783540323990

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Mechanical Modelling and Computational Issues in Civil Engineering by Michel Fremond,Franco Maceri Pdf

In this edited book various novel approaches to problems of modern civil engineering are demonstrated. Experts associated within the Lagrange Laboratory present recent research results in civil engineering dealing both with modelling and computational aspects. Many modern topics are covered, such as monumental dams, soil mechanics and geotechnics, granular media, contact and friction problems, damage and fracture, new structural materials, and vibration damping – presenting the state of the art of mechanical modelling and computational issues in civil engineering.