Preface [to] Journal of Global Optimization Vol. 40 (2008)

Abstract

Some of the papers and lectures devoted to the memory of Sergio Campanato and Guido Stampacchia, delivered during the International Conference titled 'Variational Analysis and Partial Differential Equations' held on 5-14 July 2006 are presented. The regularization theory was one of the predominant interests of Sergio Campanato, and he was concerned with the way of finding a general regularization methodology from which the regularity results in all the tough situations could be derived. He developed a methodology in which one has to study the ratio of the Lp norms on concentric balls of different radii of a solution of a class of second order differential systems depends on the ratio of the radii. Sergio searched solutions for partial differential equations by showing the existence of a unique solution of the Dirichlet problem in the class W2,p(Ω), p∈ (2 - ε, 2 + ε) and also some regularity results.