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 a Laureate Degree in 1978. He was professor at the University of Salerno from 1987 , from 1990 at the University of Naples and from 1995 at the University of Florence . Since 1999 he has been professor of mathematical analysis at the University of Naples again. He also taught at Carnegie Mellon University and the Australian National University .

Fusco dealt with, among other things, the semicontinuity of functionals in the calculus of variations, homogenization and gamma convergence , regularity of the solutions of elliptic partial differential equations, free boundary value problems, problems with freely variable discontinuities, application of the calculus of variations in image decomposition (Mumford-Shah problem), Steiner symmetrization and isoperimetric inequalities .

With Emilio Acerbi in 1981 he proved a theorem about the semi-continuity (from below) of multiple integrals in the calculus of variations, understood as functionals in Sobolew spaces , as a result of the quasi-convexity of the function occurring in the integrand. With Acerbi he proved a theorem about the partial regularity of solutions of variational problems with quasi-convex functionals.

In 2005, together with Miroslav Chlebik and Andrea Cianchi, he characterized quantities in geometric measurement theory, the diameter of which (in the sense of Renato Caccioppoli and Ennio de Giorgi ) is invariant to Steiner's symmetrization.

In a work from 2007 with Francesco Maggi and Aldo Pratelli, he succeeded in providing the first complete proof of a conjecture by RR Hall (1992) about the optimal quantitative formulation of the n-dimensional isoperimetric inequality. In the two-dimensional case, this goes back to studies by Felix Bernstein and Tommy Bonnesen in the 1920s.

He also worked with Luigi Ambrosio and Pierre-Louis Lions , among others . With Ambrosio and Diego Pallara he wrote a monograph on the calculus of variations with functions of limited variation and problems with free discontinuities (as in the Mumford-Shah problem).

Since 2007 he has been on the board of directors 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), whose Luigi Tartufari Prize 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).

Fonts

with Paolo Marcellini , Carlo Sbordone : Analisi Matematica Due. Liguori Editore, Naples 1996, ISBN 88-207-2675-0 .
with Luigi Ambrosio , Diego Pallara: Functions of bounded variations and free discontinuity problems (= Oxford Mathematical Monographs. ). Clarendon Press, Oxford et al. 2000, ISBN 0-19-850245-1 .
with Paolo Marcellini, Carlo Sbordone: Elementi di Analisi Matematica due. Versione semplificata per i nuovi corsi di laurea. Liguori Editore, Naples, 2001, ISBN 88-207-3137-1 .

Web links

Homepage

Individual evidence

↑ Born 1955. Student of Ennio de Giorgi (Laurea at the Scuola Normale Superiore in Pisa 1978), professor at the Polytechnic in Turin and then in Parma
^ Emilio Acerbi, Nicola Fusco: Semicontinuity problems in the calculus of variations. In: Archive for Rational Mechanics and Analysis. Vol. 86, No. 2, 1984, pp. 125-145, doi : 10.1007 / BF00275731 .
^ Emilio Acerbi, Nicola Fusco: A regularity theorem for minimizers of quasiconvex integrals. In: Archive for Rational Mechanics and Analysis. Vol. 99, 1987, No. 3, pp. 261-281, doi : 10.1007 / BF00284509 .
↑ Miroslav Chlebík, Andrea Cianchi, Nicola Fusco: The perimeter inequality under Steiner symmetrization: cases of equality. In: Annals of Mathematics . Vol. 162, No. 1, 2005, pp. 525-555, doi : 10.4007 / annals.2005.162.525 .
^ Nicola Fusco, Francesco Maggi, Aldo Pratelli: The sharp quantitative isoperimetric inequality. In: Annals of Mathematics. Vol. 168, No. 3, 2008, pp. 941-980, doi : 10.4007 / annals.2008.168.941 .

personal data
SURNAME	Fusco, Nicola
BRIEF DESCRIPTION	Italian mathematician
DATE OF BIRTH	August 14, 1956

[1] Born 1955. Student of Ennio de Giorgi (Laurea at the Scuola Normale Superiore in Pisa 1978), professor at the Polytechnic in Turin and then in Parma

[2] Emilio Acerbi, Nicola Fusco: Semicontinuity problems in the calculus of variations. In: Archive for Rational Mechanics and Analysis. Vol. 86, No. 2, 1984, pp. 125-145, doi : 10.1007 / BF00275731 .

[3] Emilio Acerbi, Nicola Fusco: A regularity theorem for minimizers of quasiconvex integrals. In: Archive for Rational Mechanics and Analysis. Vol. 99, 1987, No. 3, pp. 261-281, doi : 10.1007 / BF00284509 .

[4] Miroslav Chlebík, Andrea Cianchi, Nicola Fusco: The perimeter inequality under Steiner symmetrization: cases of equality. In: Annals of Mathematics . Vol. 162, No. 1, 2005, pp. 525-555, doi : 10.4007 / annals.2005.162.525 .

[5] Nicola Fusco, Francesco Maggi, Aldo Pratelli: The sharp quantitative isoperimetric inequality. In: Annals of Mathematics. Vol. 168, No. 3, 2008, pp. 941-980, doi : 10.4007 / annals.2008.168.941 .