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

Ph.D student of the XXV cycle of the Doctorate School in Environmental and Industrial Fluid Mechanics at University of Trieste (Italy)

Scientific Activity: 

My Ph.D thesis will be focused on the study of the existence, regularity and stability properties of critical points of functionals with linear growth with respect to the gradient at infinity. This functional and the associated Euler-Lagrange equations have been introduced the to describe situations where a flux limited diffusion term is used to model phenomena in which the gradient may become infinity at finite energy levels. I have worked on existence and stability results for the prescribed mean curvature/capillarity equation via lower and upper solutions and now I am looking for similar results for the evolutionary case.

Background: 

Master's Degree in Mathematics at University of Trieste (Italy) - October 2009 Thesis: "Navier Stokes Equations: different approaches on existence uniqueness and regularity" Mark: 110/110 Cum Laude. Diploma "Percorso Formativo Comune" at SISSA., Trieste (Italy) - October 2009 ( Diploma assigned on a merit base). Bachelor's Degree in Mathematics at University of Parma (Italy) - October 2007 Thesis: "Semigrups of linear operators and theirs application to partial differential equations" Mark: 110/110 Cum Laude.

Publications: 
  • F. Obersnel, P. Omari, S. Rivetti, Existence, regularity and stability properties of periodic solutions of a capillarity equation in the presence of lower and upper solutions, Nonlinear Anal. Real World Appl. 13 (2012), no. 6, 2830 - 2852.
  • 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. (2013). In press. Quaderno Matematico 624, Dipartimento di Matematica e Geoscienze, Università di Trieste (2012). Available at: http://www.dmi.units.it/pubblicazioni/Quaderni_Matematici/624_2012.pdf
  • C. Corsato, F. Obersnel, P. Omari, S. Rivetti, Positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space, . Math.Anal. Appl. (2013), no. 1, 227 - 239.
  • 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 Cont. Dyn. Syst. (2013). In press. Quaderno Matematico 628, Dipartimento di Matematica e Geoscienze, Università di Trieste (2012). Available at: http://www.dmi.units.it/pubblicazioni/Quaderni_Matematici/628_2012.pdf
  • F. Obersnel, P. Omari, S. Rivetti, Asymmetric Poincaré Inequalities and Solvability of Capillarity Problems. In preparation. Quaderno Matematico 631, Dipartimento di Matematica e Geoscienze, Università di Trieste (2013). Available at: http://www.dmi.units.it/pubblicazioni/Quaderni_Matematici/631_2013.pdf
Conferences: 
  • Capillary-type Equations", January 10, 2011 Cycle of seminars by former students of the Department of Mathematics of Parma (University of Parma)
  • "Existence, regularity and stability properties of periodic solutions of a capillarity equation in the presence of lower and upper solutions", January 10, 2012 Cycle of seminars by former students of the Department of Mathematics of Parma (University of Parma)
  • Periodic solutions of a capillarity equation in the presence of lower and upper solutions, May 31, 2012 , Universite Libre de Bruxelles (Belgium).
  • Periodic solutions of a capillarity equation in the presence of lower and upper solutions, October 23, 2012, DMG, Universita di Trieste.