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Analysis and Numerics of Partial Differential Equations

  • Book
  • © 2013

Overview

Editors:
  1. Franco Brezzi

    1. Ist. Matematica Applicata e, Tecnologie Informatiche (IMATI), CNR Pavia, Pavia, Italy

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  2. Piero Colli Franzone

    1. Dipartimento di Matematica "F. Casorati", Università degli Studi di Pavia, Pavia, Italy

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  3. Ugo Gianazza

    1. Dipartimento di Matematica "F. Casorati", Università degli Studi di Pavia, Pavia, Italy

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  4. Gianni Gilardi

    1. Dipartimento di Matematica "F. Casorati", Università degli Studi di Pavia, Pavia, Italy

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  • It is the first time a comprehensive survey of Magenes' activity in Mathematics is presented
  • Although from a particular point of view, it is a general perspective of the research in Partial Differential Equations and their applications developed in Italy in the period 1950-2000
  • It shows the far reaching consequences that ideas, methods, techniques originally set forth by Magenes and his school still have on Mathematics today
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer INdAM Series (SINDAMS)

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Table of contents (17 chapters)

  1. Front Matter

    Pages I-XIII
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  2. A Historical Perspective

    1. Front Matter

      Pages 1-1
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    2. Personal Memories

      • Franco Brezzi
      Pages 3-4

    3. Some Aspects of the Research of Enrico Magenes in Partial Differential Equations

      • Giuseppe Geymonat
      Pages 5-11

    4. Enrico Magenes and the Dam Problem

      • Claudio Baiocchi
      Pages 13-18

    5. Inverse Problems in Electrocardiology

      • Piero Colli Franzone
      Pages 19-36

    6. Stefan Problems and Numerical Analysis

      • Claudio Verdi
      Pages 37-45

    7. Enrico Magenes and the Teaching of Mathematics

      • Mario Ferrari
      Pages 47-52

    8. List of Mathematical Works Authored or Edited by Enrico Magenes

      • Ugo Gianazza
      Pages 53-59

  3. Recent Developments

    1. Front Matter

      Pages 61-61
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    2. Heat Flow and Calculus on Metric Measure Spaces with Ricci Curvature Bounded Below—The Compact Case

      • Luigi Ambrosio, Nicola Gigli, Giuseppe Savaré
      Pages 63-115

    3. Spaces of Finite Element Differential Forms

      • Douglas N. Arnold
      Pages 117-140

    4. A Priori Bounds for Solutions of a Nonlocal Evolution PDE

      • Luis Caffarelli, Enrico Valdinoci
      Pages 141-163

    5. On the Numerical Analysis of Adaptive Spectral/hp Methods for Elliptic Problems

      • Claudio Canuto, Marco Verani
      Pages 165-192

    6. A Theory and Challenges for Coarsening in Microstructure

      • Katayun Barmak, Eva Eggeling, Maria Emelianenko, Yekaterina Epshteyn, David Kinderlehrer, Richard Sharp et al.
      Pages 193-220

    7. A Generalized Empirical Interpolation Method: Application of Reduced Basis Techniques to Data Assimilation

      • Yvon Maday, Olga Mula
      Pages 221-235

    8. Analysis and Numerics of Some Fractal Boundary Value Problems

      • Umberto Mosco
      Pages 237-255

    9. AFEM for Geometric PDE: The Laplace-Beltrami Operator

      • Andrea Bonito, J. Manuel Cascón, Pedro Morin, Ricardo H. Nochetto
      Pages 257-306

    10. Generalized Reduced Basis Methods and n-Width Estimates for the Approximation of the Solution Manifold of Parametric PDEs

      • Toni Lassila, Andrea Manzoni, Alfio Quarteroni, Gianluigi Rozza
      Pages 307-329

    11. Variational Formulation of Phase Transitions with Glass Formation

      • Augusto Visintin
      Pages 331-365
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About this book

This volume is a selection of contributions offered by friends, collaborators, past students in memory of Enrico Magenes. The first part gives a wide historical perspective of Magenes' work in his 50-year mathematical career; the second part contains original research papers, and shows how ideas, methods, and techniques introduced by Magenes and his collaborators still have an impact on the current research in Mathematics.

Editors and Affiliations

  • Ist. Matematica Applicata e, Tecnologie Informatiche (IMATI), CNR Pavia, Pavia, Italy

    Franco Brezzi

  • Dipartimento di Matematica "F. Casorati", Università degli Studi di Pavia, Pavia, Italy

    Piero Colli Franzone, Ugo Gianazza, Gianni Gilardi

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