Nicola Fusco
Nicola Fusco ( born August 14, 1956) is an Italian mathematician who deals with the calculus of variations and partial differential equations.
Fusco studied mathematics at the University of Naples with the Laurea degree in 1978., He worked from 1987 professor at the University of Salerno, from 1990 at the University of Naples and from 1995 at the University of Florence. Since 1999, he is again a professor of mathematical analysis at the University of Naples. He also taught at Carnegie Mellon University and the Australian National University.
Fusco dealt among other things with semicontinuity of functionals in the calculus of variations, homogenization and Gamma - convergence, regularity of solutions of elliptic partial differential equations, free boundary value problems, problems with free variable discontinuity, application of the calculus of variations in the image decomposition ( Mumford - Shah problem), Steiner symmetrization and Isoperimetric inequalities.
With Emilio Acerbi 1981 he proved a theorem on the semi-continuity (from below) of multiple integrals in the calculus of variations, considered as functionals in Sobolev spaces, as a result of the quasiconvexity occurring in the integrand function. With Acerbi he proved a theorem on the partial regularity of solutions of variational problems with quasiconvex functionals.
In 2005, he characterized with Miroslav Chlebik and Andrea Cianchi quantities in geometric measure theory, the diameter (in the sense of Renato Caccioppoli and Ennio de Giorgi ) invariant with respect to Steiner symmetrization is.
In a work from 2007 with Francesco Maggi and Aldo Pratelli he managed the first complete proof of a conjecture of RR Hall ( 1992) on the optimal quantitative formulation of the n-dimensional isoperimetric inequality .. In the two-dimensional case that goes up on studies by Felix Bernstein and Tommy BONNESEN back in the 1920s.
In addition, he worked with, among others, with Luigi Ambrosio and Pierre -Louis Lions. With Ambrosio and Diego Pallara he wrote a monograph on the calculus of variations with functions limited variation and free discontinuity problems (as in the Mumford - Shah problem).
Since 2007, he Leitungsrat of the Istituto Nazionale di Alta Matematica. He is the editor of Advances in Calculus of Variations.
In 1994 he received the Premio Caccioppoli. He is a member of the Accademia dei Lincei (2010), the price of Luigi Tartufari he received in 2010. He was invited speaker at the International Congress of Mathematicians 2010 in Hyderabad ( Equilibrium configurations of epitaxially strained elastic films: existence, regularity and qualitative properties of solutions ) and at the European Congress of Mathematicians 2008 in Amsterdam (The sharp Sobolev inequality in quantitative form).
Writings
- With Luigi Ambrosio, Diego Pallara Functions of bounded variations and free discontinuity problems, Oxford Mathematical Monographs, Oxford, Clarendon Press 2000
- With Paolo Marcellini, Sbordone Carlo: Analisi Matematica Due, Liguori Editore, Naples, 1996
- With Paolo Marcellini, Sbordone Carlo: Elementi di Analisi Matematica due, Liguori Editore, Naples, 2001