Giuseppe Mingione | |
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| Born | 28 August 1972 |
| Nationality |  Italy |
| Alma mater | University of Naples Federico II |
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| Awards | Bartolozzi Prize (2005) Stampacchia Medal (2006) Caccioppoli Prize (2010) |
| Scientific career | |
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| Institutions | University of Parma |
| Doctoral advisor | Nicola Fusco |
Giuseppe Mingione (born 28 August 1972) is an Italian mathematician who is active in the fields of partial differential equations and calculus of variations.
Mingione received his Ph.D. in mathematics from the University of Naples Federico II in 1999 having Nicola Fusco as advisor; he is professor of mathematics at the University of Parma. He has mainly worked on regularity aspects of the Calculus of Variations, solving a few longstanding questions about the Hausdorff dimension of the singular sets of minimisers of vectorial integral functionals and the boundary singularities of solutions to nonlinear elliptic systems. [1] This connects to the work of authors as Almgren, De Giorgi, Morrey, Giusti, who proved theorems asserting regularity of solutions outside a singular set (i.e. a closed subset of null measure) both in geometric measure theory and for variational systems of partial differential equations. These are indeed called partial regularity results and one of the main issues is to establish whether the dimension of the singular set is strictly less than the ambient dimension. This question has found a positive answer for general integral functionals, thanks to the work of Kristensen and Mingione, who have also given explicit estimates for the dimension of the singular sets of minimisers. [2] [3] Subsequently, Mingione has worked on nonlinear potential theory obtaining potential estimates for solutions to nonlinear elliptic and parabolic equations. Such estimates allow to give a unified approach to the regularity theory of quasilinear, degenerate equations [4] [5] [6] and relate to and upgrade previous work of Kilpeläinen, Malý, Trudinger, Wang.
Mingione was awarded the Bartolozzi prize in 2005, the Stampacchia medal in 2006 and the Caccioppoli prize in 2010. In 2007 he was awarded an ERC grant. [7] Mingione is listed as an ISI highly cited researcher [8] and was invited to deliver the Nachdiplom Lectures in 2015 at ETH Zürich. [9] He was invited speaker at the 2016 European Congress of Mathematics in Berlin. [10] In 2017 he was appointed Commander of the Order of Merit of the Italian Republic by the President of the Italian Republic. [11]
The calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations.
The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450. It is awarded every three years for a notable research work in analysis that has appeared during the past six years. The work must be published in a recognized, peer-reviewed venue. The current award is $5,000.
Ennio De Giorgi was an Italian mathematician who worked on partial differential equations and the foundations of mathematics.
Louis Nirenberg was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.
Hilbert's nineteenth problem is one of the 23 Hilbert problems, set out in a list compiled by David Hilbert in 1900. It asks whether the solutions of regular problems in the calculus of variations are always analytic. Informally, and perhaps less directly, since Hilbert's concept of a "regular variational problem" identifies this precisely as a variational problem whose Euler–Lagrange equation is an elliptic partial differential equation with analytic coefficients, Hilbert's nineteenth problem, despite its seemingly technical statement, simply asks whether, in this class of partial differential equations, any solution inherits the relatively simple and well understood property of being an analytic function from the equation it satisfies. Hilbert's nineteenth problem was solved independently in the late 1950s by Ennio De Giorgi and John Forbes Nash, Jr.
Lawrence Craig Evans is an American mathematician and Professor of Mathematics at the University of California, Berkeley.
Leon Melvyn Simon, born in 1945, is a Leroy P. Steele Prize and Bôcher Prize-winning mathematician, known for deep contributions to the fields of geometric analysis, geometric measure theory, and partial differential equations. He is currently Professor Emeritus in the Mathematics Department at Stanford University.
Luigi Ambrosio is a professor at Scuola Normale Superiore in Pisa, Italy. His main fields of research are the calculus of variations and geometric measure theory.
Nicola Fusco is an Italian mathematician mainly known for his contributions to the fields of calculus of variations, regularity theory of partial differential equations, and the theory of symmetrization. He is currently professor at the Università di Napoli "Federico II". Fusco also taught and conducted research at the Australian National University at Canberra, the Carnegie Mellon University at Pittsburgh and at the University of Florence.
Enrico Giusti was an Italian mathematician mainly known for his contributions to the fields of calculus of variations, regularity theory of partial differential equations, minimal surfaces and history of mathematics. He was professor of mathematics at the Università di Firenze; he also taught and conducted research at the Australian National University at Canberra, at the Stanford University and at the University of California, Berkeley. After retirement, he devoted himself to the managing of the "Giardino di Archimede", a museum entirely dedicated to mathematics and its applications. Giusti was also the editor-in-chief of the international journal dedicated to the history of mathematics Bollettino di storia delle scienze matematiche.
The Mumford–Shah functional is a functional that is used to establish an optimality criterion for segmenting an image into sub-regions. An image is modeled as a piecewise-smooth function. The functional penalizes the distance between the model and the input image, the lack of smoothness of the model within the sub-regions, and the length of the boundaries of the sub-regions. By minimizing the functional one may compute the best image segmentation. The functional was proposed by mathematicians David Mumford and Jayant Shah in 1989.
Mariano Giaquinta, is an Italian mathematician mainly known for his contributions to the fields of calculus of variations and regularity theory of partial differential equation. He is currently professor of Mathematics at the Scuola Normale Superiore di Pisa and he is the director of De Giorgi center at Pisa.
Alessio Figalli is an Italian mathematician working primarily on calculus of variations and partial differential equations.
Andrea Malchiodi is an Italian mathematician who is active in the fields of partial differential equations and calculus of variations, with several contributions to geometric analysis.
Camillo De Lellis is an Italian mathematician who is active in the fields of calculus of variations, hyperbolic systems of conservation laws, geometric measure theory and fluid dynamics. He is a permanent faculty member in the School of Mathematics at the Institute for Advanced Study. He is also one of the two managing editors of Inventiones Mathematicae.
Gianni Dal Maso is an Italian mathematician who is active in the fields of partial differential equations, calculus of variations and applied mathematics.
Michael Struwe is a German mathematician who specializes in calculus of variations and nonlinear partial differential equations. He won the 2012 Cantor medal from the Deutsche Mathematiker-Vereinigung for "outstanding achievements in the field of geometric analysis, calculus of variations and nonlinear partial differential equations".
Tristan Rivière is a French mathematician, working on partial differential equations and the calculus of variations.
Xavier Ros Oton is a Spanish mathematician who works on partial differential equations (PDEs). He is an ICREA Research Professor and a Full Professor at the University of Barcelona.
Ulisse Stefanelli is an Italian mathematician. He is currently professor at the Faculty of Mathematics of the University of Vienna. His research focuses on calculus of variations, partial differential equations, and materials science.
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