Analysis and Numerics of Partial Differential Equations

The first comprehensive presentation of Magenes' work in mathematics, this book covers the research into PDEs and their applications developed in Italy in the second half of the twentieth century. It shows just how much Magenes and his school contributed.

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.

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

Inhalt

Part I A Historical Perspective.- Personal Memories.- Some Aspects of the Research of Enrico Magenes in Partial Differential Equations.- Enrico Magenes and the Dam Problem.- Inverse Problems in Electrocardiology.- Stefan Problems and Numerical Analysis.- Enrico Magenes and the Teaching of Mathematics.- List of Mathematical Works Authored or Edited by Enrico Magenes.- Part II Recent Developments.- Heat Flow and Calculus on Metric Measure Spaces with Ricci Curvature Bounded Below - the Compact Case.- Spaces of Finite Element Differential Forms.- A Priori Bounds for Solutions of a Nonlocal Evolution PDE.- On the Numerical Analysis of Adaptive Spectral/hp Methods for Elliptic Problems.- A Theory and Challenges for Coarsening in Microstructure.- A Generalized Empirical Interpolation Method: Application of Reduced Basis Techniques to Data Assimilation.- Analysis and Numerics of Some Fractal Boundary Value Problems.- AFEM for Geometric PDE: The Laplace-Beltrami Operator.- Generalized Reduced Basis Methods and n-Width Estimates for the Approximation of the Solution Manifold of Parametric PDEs.- Variational Formulation of Phase Transitions with Glass Formation.