Analysis and Numerics of Partial Differential Equations

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

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.

• Applications
• Calculus of Variations
• Numerics
• Partial Differential Equations

• 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

Policies and ethics