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A Pure Soul
This biography illuminates the life of Ennio De Giorgi, a mathematical genius in parallel with John Nash, the Nobel Prize Winner and protagonist of A Beautiful Mind. Beginning with his childhood and early years of research, into his solution of the 19th problem of Hilbert and his professorship, this book pushes beyond De Giorgi’s rich contributions to the mathematics community, to present his work in human rights, including involvement in the fight for Leonid Plyushch’s freedom and the defense of dissident Uruguayan mathematician José Luis Massera. Considered by many to be the greatest Italian analyst of the twentieth century, De Giorgi is described in this volume in full through documents and direct interviews with friends, family, colleagues, and former students.
An Introduction to Sobolev Spaces and Interpolation Spaces
After publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience.
Elliptic and Parabolic Problems
Haim Brezis has made significant contributions in the fields of partial differential equations and functional analysis. He is an inspiring teacher and counsellor of many mathematicians in the front ranks. The collection of papers presented in this volume, reflect Brezis's elegant way of creative thinking.
Recent Trends in Nonlinear Partial Differential Equations I
This book is the first of two volumes which contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honor of Patrizia Pucci's 60th birthday. The workshop brought t
The General Theory of Homogenization
Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science, new mathematical tools must be introduced, like the author’s H-measures, variants by Patrick Gérard, and others yet to be discovered.
An Introduction to Navier-Stokes Equation and Oceanography
This text corresponds to a graduate mathematics course taught at Carnegie Mellon University in the spring of 1999. Included are comments added to the lecture notes, a bibliography containing 23 items, and brief biographical information for all scientists mentioned in the text, thus showing that the creation of scientific knowledge is an international enterprise.
Partial Differential Equations and the Calculus of Variations
The Italian school of Mathematical Analysis has long and glo rious traditions. In the last thirty years it owes very much to the scientific pre-eminence of Ennio De Giorgi, Professor of Mathemati cal Analysis at the Scuola Normale Superiore di Pisa. His fundamental theorems in Calculus of Variations, in Minimal Surfaces Theory, in Partial Differential Equations, in Axiomatic Set Theory as well as the fertility of his mind to discover both general mathematical structures and techniques which frame many different problems, and profound and meaningful examples which show the limits of a theory and give origin to new results and theories, makes him an absolute reference point for all Italian mat...
Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48)
This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order diverge...
Asymptotic Analysis for Periodic Structures
This is a reprinting of a book originally published in 1978. At that time it was the first book on the subject of homogenization, which is the asymptotic analysis of partial differential equations with rapidly oscillating coefficients, and as such it sets the stage for what problems to consider and what methods to use, including probabilistic methods. At the time the book was written the use of asymptotic expansions with multiple scales was new, especially their use as a theoretical tool, combined with energy methods and the construction of test functions for analysis with weak convergence methods. Before this book, multiple scale methods were primarily used for non-linear oscillation proble...
Calculus of Variations, Applications and Computations
This research presents some important domains of partial differential equations and applied mathematics including calculus of variations, control theory, modelling, numerical analysis and various applications in physics, mechanics and engineering. These topics are now part of many areas of science and have experienced tremendous development during the last decades.
