Giuseppe Mingione

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

Mingione graduated from the University of Naples with the Laurea degree in 1994 and his doctorate at Nicola Fusco 1998. Has carried out research since 1996 at the University of Parma, was there from 2001 assistant professor and in 2005 professor of Analysis.

It deals with the calculus of variations and partial differential equations, especially with Regularitätsproblemen in the calculus of variations, where minimizers of integral functionals are looking for, and in solutions of elliptic and parabolic partial differential equations in the founded by Ennio De Giorgi in the 1960s, problems concerning the partial regularity ie regularity except for a singular set of measure 0 He sparked a since the late 1970s open question with respect to the Hausdorff dimension of the singular set, 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 gave Mingione estimates for the dimension of the singular sets.

In 2006 he received the Stampacchia Medal, 2005 Bartolozzi Prize of the UMI and 2010 the Caccioppoli Prize. In 2007 he received an Advanced Grant from the European Research Council ( ERC). In 2008 he was Plenarsprecher at the Annual Meeting of the DMV and 2011 the UMI in Bologna, each with non-linear Calderon - Zygmund theory.

Writings

  • 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
  • Jan Kristensen: The singular set of minima of integral functionals, Archive for Rational Mechanics & Analysis, Volume 180, 2006, p.331 -398
  • Frank Duzaar Jan Kristensen: The existence of regular boundary points for non- linear elliptic systems, Journal of Pure and Applied Mathematics ( Crelle's Journal ), Volume 602, 2007, pp. 17-58
  • Jan Kristensen: Boundary regularity in variational problems, Archive for Rational Mechanics & Analysis, Volume 198, 2010, pp. 369-455
  • Jan Kristensen: The singular set of minima of multiple integrals lipschitzian, Archive for Rational Mechanics & Analysis, Volume 184, 2007, pp. 341-369
  • 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 Mathematical Society, Volume 112, 2010, pp. 159-191
  • Gradient potential estimates, Journal of the European Mathematical Society, Volume 13, 2011, p 459-486
  • Frank Duzaar, Klaus Steffen: Parabolic systems with polynomial growth and regularity, American Mathematical Society, 2011.
  • With T. Kuusi: Linear potentials in nonlinear potential theory, Archive for Rational Mechanics and Analysis, Volume 207, 2013, pp. 215-246
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