EMS Lectures

Biography of Professor Gianni Dal Maso (EMS Lecturer of 2002)

Professor Dal Maso was born in Vicenza in 1954; in 1955 his family moved to Trieste, where he had his basic education. He was a student of the Scuola Normale of Pisa from 1973 to 1977, and graduated in Mathematics from the University of Pisa in 1977, with Ennio De Giorgi as his advisor. He was then a graduate student of the Scuola Normale di Pisa from 1978 to 1981, working with Professor Ennio De Giorgi on many problems connected with the theory of gamma-convergence, that was developed in those years.

After serving as assistant professor of Mathematical Analysis in the Faculty of Engineering of the University of Udine from 1982 to 1985, he moved to the International School for Advanced Studies (SISSA) in Trieste. He worked there as associate professor of Mathematical Analysis from 1985 to 1987, and as full professor of Calculus of Variations since 1987. He was awarded the Caccioppoli Prize in 1991 and the ``Medaglia dei XL per la Matematica'' of the ``Accademia Nazionale delle Scienze detta dei XL'' in 1996.

At SISSA he has developed his research interests on gamma-convergence, homogenization theory, and free discontinuity problems, and has been the supervisor of 19 Ph.D. students working on these subjects. At present he serves as the head of the Sector of Functional Analysis and Applications of SISSA.

Research interests

Professor Dal Mason started his research work in Pisa while Ennio De Giorgi was developing the new notion of gamma-convergence to deal in a systematic way with the following kind of phenomena: the solutions of variational problems depending on a parameter may converge to the solution of a limit problem even if the integrands of the functionals to be minimized do not converge in any reasonable sense, or converge to a limit integrand which is different from the integrand of the functional minimized by the limit of the solutions. Gamma-convergence is a very efficient tool to tackle this kind of problems.

In his work in Pisa and in Udine he studied several problems related to gamma-convergence. In particular he developed, together with Giuseppe Buttazzo, several techniques to prove, under different hypotheses, that the gamma-limits of integral functionals are still integral functionals, and I studied, by gamma-convergence techniques, the asymptotic behaviour of solutions to minimum problems with strongly oscillating obstacles. Using the notion of capacity, he also gave a complete characterization of the sequences of obstacle problems whose variational limit is still an obstacle problem.

He later used these techniques to study, together with Umberto Mosco, the asymptotic behaviour of the solutions of Dirichlet problems for the Laplace equation in perforated domains, and to determine the general form of their variational limits, as well as the fine properties of the solutions of these limit problems. These results have been extended, with different collaborators, to the case of other linear and nonlinear equations and systems.

At present his main research interests are in free discontinuity problems. These are variational problems where the functional to be minimized depends on a function and on its discontinuity set, whose shape and location are not prescribed. In many cases the discontinuity set can be considered as the main unknown of the problem. Examples are given by the minimization of the Mumford-Shah functional in image segmentation, and by the minimum problems which appear in many variational models for fracture mechanics, where the unknown crack is represented as the discontinuity set of the displacement vector, and the functional to be minimized is the sum of the elastic energy and of an integral on the discontinuity set, which represents the work done to produce the crack.

Selected list of publications

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Last change: February 5, 2002

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