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Cycle: 
26 cycle
Tutor: 
Prof. Pierpaolo Omari
Curriculum, Annual Report, Thesis: 
Current Position: 

Ph.D. student in Environmental and Industrial Fluid Mechanics, University of Trieste.

Scientific Activity: 

My research program concerns the study of boundary value problems for quasilinear elliptic equations, involving the Euclidean or the Minkowski mean curvature operator. Namely, the following problems have been treated:

1. the periodic problem associated with the one-dimensional prescribed curvature equation in the Euclidean space. The equation arises when dealing with capillarity phenomena.

2. The homogeneous Dirichlet problem associated with an anisotropic prescribed mean curvature equation in the Euclidean space. Such a problem has been recently proposed as a model for the geometrical description of the human cornea.

3. The homogeneous Dirichlet problem associated with a prescribed mean curvature equation in the Minkowski space. The problem is of great interest in general relativity and differential geometry.

The techniques used are topological or variational, in particular they rely on degree theory or on critical point theory, respectively.

Background: 

Master degree in Mathematics, University of Udine, October 20th 2010, Thesis' title: Problemi ai limiti per equazioni differenziali fortemente non lineari (Boundary-value problems for strongly nonlinear differential equations), mark: 110/110 cum laude.

Publications: 
  • C. Corsato, C. De Coster, P. Omari: The Dirichlet problem for a prescribed anisotropic mean curvature equation: existence, uniqueness and regularity of solutions, work in progress.
  • C. Corsato, C. De Coster, P. Omari: Radially symmetric solutions of an anisotropic mean curvature equation modeling the corneal shape, Discrete Contin. Dyn. Syst., in press.
  • C. Corsato, P. Omari, F. Zanolin: Subharmonic solutions of the prescribed curvature equation, Commun. Contemp. Math., in press.
  • I. Coelho, C. Corsato, P. Omari: A one-dimensional prescribed curvature equation modeling the corneal shape, Bound. Value Prob. 2014,   2014:127.
  • C. Corsato, F. Obersnel, P. Omari, S. Rivetti: On the lower and upper solution method for the prescribed mean curvature equation in Minkowski space, Discrete Contin. Dyn. Syst. (2013), Supplement 2013 (2013), 159-169.
  • C. Corsato, F. Obersnel, P. Omari, S. Rivetti: Positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space, J. Math. Anal. Appl. 405 (2013), no. 1, 227-239.
  • I. Coelho, C. Corsato, S. Rivetti: Positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation in a ball, Topol. Methods Nonlinear Anal. 44 (2014), 23-40.
  • I. Coelho, C. Corsato, F. Obersnel, P. Omari: Positive solutions of the Dirichlet problem for the one-dimensional Minkowski-curvature equation, Adv. Nonlinear Stud. 12 (2012), 621-638.
Conferences: 

October 10, 2014: Journée  du Laboratoire Painlevé et de la Fédération (Fédération de Recherche Mathématique du Nord - Pas de Calais), Université de Lille 1 (France).

October 6 - 7, 2014: Neuvièmes Journées EDP, Lille - Littoral - Valenciennes, Université de Lille 1 (France).

July 7 - 11, 2014: 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Universidad Autónoma de Madrid (Spain).

May 28 - 30, 2014: NPDE 2014, Recent Trends in Nonlinear Partial Differential Equations and Applications, Università degli Studi di Trieste.

November 26, 2013: Nonlinear Problems with Singular Data, Accademia Nazionale dei Lincei, Roma.

October 28 - 31, 2013: Nord Pas de Calais/Belgium Congress of mathematics, Université de Valenciennes et du Hainaut - Cambrésis (France) and Université de Mons (Belgium).

January 30 - February 1, 2013: QTNDE 2013, Qualitative Theory of Nonlinear Differential Equation, Università degli Studi di Trieste.

May 30 - June 6, 2012: Spring School in Nonlinear Partial Differential Equations, Université libre de Bruxelles (Belgium).

June 20 - 25, 2011: School on Stability and Bifurcation for Nonautonomous Differential Equations, International Mathematical Summer Center, Cetraro.