Progress in Nonlinear Differential Equations and Their Applications
2 primary works
Book 5
Composite Media and Homogenization Theory
by Gianni Dal Maso and Gianfausto Dell'Antonio
Published February 1991
For mathematicians and engineers interested in modeling the behavior of composite and random media, surveys recent advances using such mathematical techniques as partial differential equations and the calculus of variations. The 14 papers were originally presented at a workshop in Trieste, Italy, Ja
Book 8
The last twentyfive years have seen an increasing interest for variational convergences and for their applications to different fields, like homogenization theory, phase transitions, singular perturbations, boundary value problems in wildly perturbed domains, approximation of variatonal problems, and non- smooth analysis. Among variational convergences, De Giorgi's r-convergence plays a cen- tral role for its compactness properties and for the large number of results concerning r -limits of integral functionals. Moreover, almost all other varia- tional convergences can be easily expressed in the language of r -convergence. This text originates from the notes of the courses on r -convergence held by the author in Trieste at the International School for Advanced Studies (S. I. S. S. A. ) during the academic years 1983-84,1986-87, 1990-91, and in Rome at the Istituto Nazionale di Alta Matematica (I. N. D. A. M. ) during the spring of 1987. This text is far from being a treatise on r -convergence and its appli- cations.