Giuseppe Mingione

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Giuseppe Mingione (2019)

Giuseppe Mingione (born August 28, 1972 in Caserta ) is an Italian mathematician.

Mingione studied at the University of Naples with a laureate degree in 1994 and a doctorate with Nicola Fusco in 1999. He carried out research at the University of Parma from 1996 , where he was assistant professor from 2001 and from 2005 professor of analysis.

He deals with the calculus of variations and partial differential equations , especially with regularity problems in the calculus of variations, where minimizers of integral functionals are sought, and with the solutions of elliptic and parabolic partial differential equations in the problem area of partial regularity founded by Ennio de Giorgi in the 1960s , That is, regularity down to a singular set of measure 0. He solved a question about the Hausdorff dimension of this singular set that had been open since the late 1970s, in particular the positive answer to the question whether the dimension of the singular set is smaller than that of the surrounding space . Together with Jan Kristensen, Mingione gave estimates for the dimensions of the singular sets.

In 2004 he was Von Staudt visiting professor at the University of Erlangen-Nuremberg. In 2006 he received the Stampacchia Medal , in 2005 the Bartolozzi Prize of the UMI, in 2010 the Caccioppoli Prize and in 2016 the Amerio Prize of the Istituto Lombardo Accademia di Scienze e Lettere . In 2007 he received an Advanced Grant from the European Research Council (ERC). In 2008 he was plenary speaker at the general assembly of the DMV and in 2011 that of the UMI in Bologna, each on non-linear Calderon-Zygmund theory. In 2016 he was invited speaker at the European Congress of Mathematicians in Berlin. In 2017 he became Commander of the Order of Merit of the Italian Republic.

Fonts

  • The singular set of solutions to non-differentiable elliptic systems, Archive for Rational Mechanics & Analysis, Volume 166, 2003, pp. 287-301.
  • Bounds for the singular sets of solutions of non linear elliptic systems, Calculus of Variations and Partial Differential Equations, Volume 18, 2003, 373-400
  • with Jan Kristensen: The singular set of minima of integral functionals, Archive for Rational Mechanics & Analysis, Volume 180, 2006, pp. 331–398
  • with Frank Duzaar, Jan Kristensen: The existence of regular boundary points for non-linear elliptic systems, Journal for pure and applied mathematics (Crelles Journal), Volume 602, 2007, pp. 17–58
  • with Jan Kristensen: Boundary regularity in variational problems, Archive for Rational Mechanics & Analysis, Volume 198, 2010, pp. 369–455
  • with Jan Kristensen: The singular set of lipschitzian minima of multiple integrals, Archive for Rational Mechanics & Analysis, Volume 184, 2007, pp. 341-369
  • with E. Acerbi: Gradient estimates for a class of parabolic systems, Duke Mathematical Journal, Volume 136, 2007, pp. 285-320
  • The Calderón-Zygmund theory for elliptic problems with measure data, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (Ser. V), Volume 6, 2007, pp. 195-261
  • Regularity of minima, an invitation on the dark side of the calculus of variations, Applications of Mathematics, Volume 51, 2006, pp. 355-426
  • Nonlinear Aspects of Calderon-Zygmund Theory, Annual Report of the German Mathematicians Association, Volume 112, 2010, pp. 159–191
  • Gradient potential estimates, Journal of the European Mathematical Society, Volume 13, 2011, pp. 459-486
  • with Frank Duzaar, Klaus Steffen : Parabolic systems with polynomial growth and regularity , Memoirs of the American Mathematical Society, Volume 214, no.1005, 2011.
  • with T. Kuusi: Linear potentials in nonlinear potential theory, Archive for Rational Mechanics and Analysis, Volume 207, 2013, pp. 215–246

Web links

Individual evidence

  1. ^ Mariano Giaquinta Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems , Annals of Mathematical Studies, Princeton University Press 1983
  2. ↑ Laudatory speech
  3. ↑ Amerio Prize 2016 ( Memento of the original from February 13, 2017 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice.  @1@ 2Template: Webachiv / IABot / www.istitutolombardo.it
personal data
SURNAME Mingione, Giuseppe
BRIEF DESCRIPTION Italian mathematician
DATE OF BIRTH August 28, 1972
PLACE OF BIRTH Caserta