• We apply variational and topological methods in order to obtain solutions of nonlinear elliptic equations as the mean curvature equation and related systems, and boundary value problems for the p-laplacian. We are interested in existence, uniqueness and regularity of the solutions.

• We study systems of ordinary differential equations using Leray-Schauder continuation methods and degree theory. In particular, we study the existence of periodic solutions of Duffing-type equations and the general forced pendulum equation. We also apply numerical methods as finite differences and finite elements.

• We study existence and uniqueness for the stationary and evolution problems related to transport fenomena models in semiconductors, and other equations that arise in Physics as Navier-Stokes equation, Schrödinger equation and the equations for the wave propagation in different media.

• We study convergence of singular perturbations in free boundary problems such as the equations for minimal surfaces and phase transition models.

• We study parabolic nonlinear equations by numerical methods. We obtained the thermal conductivity and diffusivity of rubber compound and its dependence with the temperature. We also studied the influence of the carbon black dispersion on the thermal diffusivity of an SBR vulcanizate using finite elements and the shooting method.

• We study the mathematical properties of gauge transformations with respect to the Coulomb's gauge by variational analysis of an energy functional. We determinate molecular properties by minimizing the associated energy functional.

• We study the existence of solutions for equations arising in financial models, like Black-Scholes Equation. We apply numerical and topological methods. In particular, we apply iterative procedures of Newton Imbedding-type.

P Amster, M. C. Mariani and D. Rial.

Nonlinear Analysis 42 (2000), 673-77.
 
 

2. Solutions to the mean cuvature equation by fixed point methods.

M. C. Mariani and D. Rial.

Bulletin of The Belgian Mathematical Society 4 (1997), 1-4.
 
 

3. Resolution of Semilinear Equations by Fixed Point Methods.

P. Amster and M. C. Mariani.

Bulletin of The Belgian Mathematical Society 7 (2000), 215-220
 
 

4. The prescribed mean curvature equation with Dirichlet conditions.

P. Amster and M. C. Mariani.

Nonlinear Analysis 44 (2001), 59-64.
 
 

5. Solutions to general quasilinear elliptic second order problems.

P. Amster, M. M. Cassinelli and M. C. Mariani.

Nonlinear Studies 7 Nº2, 2000, 283-289.
 
 

6. An improvement in the determination of thermal properties of elastomeric compounds.

M. C. Mariani, M. P. Beccar Varela and A. J. Marzocca.

KGK Kautschuk Gummi Kunststoffe, Vol. 50, p. 39-42, 1997.
 
 

7. Influence of the carbon black dispersion in the thermal diffusivity of SBR vulcanizates.

S. Goyanes, M. P. Beccar Varela, M. C. Mariani, A. J. Marzocca.

Journal of Applied Polymer Sciences, Vol. 72, 1379-1385, 1999.
 
 

8. Existence and regularity of weak solutions to the prescribed mean curvature equation for a nonparametric surface.

P. Amster, M. Cassinelli, M. C. Mariani and D.F. Rial.

Abstract and Applied Analysis, Vol 4 (1) 1999.
 
   

9. Solutions to the prescribed mean curvature equation with Dirichlet conditions by variational methods.

P. Amster, P. De Napoli and M. C. Mariani.

Proyecciones 18, 2 (1999), 155-164.
 
 

10. Magnetic susceptibility minimization respect to the gauge.

M. P. Beccar Varela, C. Caputo, M. Ferraro, P. Lazzeretti, M. C. Mariani and D. Rial.

International Journal of Quantum Chemistry , Vol 77, 599-606 (2000).
 
 

11. Solutions to the mean curvature equation for nonparametric surfaces by fixed point methods.

P. Amster, J.P. Borgna, M. C. Mariani, and D.F. Rial.

Revista de la Unión Matemática Argentina, Vol.41, 3, 1999, 15-21.
 
 

12. Solutions to quasilinear equations by an iterative method.

P. Amster, M. M. Cassinelli and M. C. Mariani.

Bulletin of the Belgian Mathematical Society 7 (2000), 435-441.
 
 

13. Weak solutions of the derivative nonlinear Schrödinger Equation.

D. Rial.

Nonlinear Analysis 49A, 2, 149-158.
 
 

14. Solutions of H-systems using the Green function.

P. Amster, M.C. Mariani and D. Rial.

Bulletin of the Belgian Mathematical Society 7 (2000), 487-492.
 
 

15. A boundary value problem for a semilinear second order ODE.

P. Amster, M.C.Mariani and J. Sabia

Revista de la Unión Matemática Argentina 41 Nº4 (2000), 61-68.
 
 

16. A boundary value problem in the hyperbolic space.

P. Amster, G. Keilhauer and M..Mariani

Abstract and Applied Analysis, Vol 4 (4) 1999.
 
   

17. An iteration procedure for nonlinear boundary conditions.

P. Amster and M.C.Mariani

Revista de la Unión Matemática Argentina 42 Nº1 (2000), 9-16.
 
 

18. Subsonic solutions to a one-dimensional non-isentropic hydrodynamic model for semiconductors.

P.Amster, M.P. Beccar Varela, A. Jüngel y M.C.Mariani.

Journal of Mathematical Analysis and Applications 258 (2001), 52-62.
 
 

19. Nonlinearities in a second order O.D.E.

P.Amster.

Electronic Journal of Differencial Equations 2001, pp. 13-21.
 
 

20. Dirichlet and periodic-type conditions for a Painlevé II Equation

P.Amster, M.C.Mariani and C. Rogers.

Journal of Mathematical Analysis and Applications 265 (2002), 1-11.
 
 

21. Existence results for the mean curvature equation.

P.Amster and M.C.Mariani

Journal of Nonlinear Analysis: Series A Theory and Methods 47 (2001) 4845-4848.

22. Three solutions for quasilinear equations in Rⁿ near resonance.

P. De Nápoli and M.C.Mariani.

Electronic Journal of Differencial Equations, 2001, pp. 131-140.
 
 
 

23. Solvability and uniqueness results for equations of mean curvature type.

P.Amster and M.C.Mariani.

Revista de la Unión Matemática Argentina 42 Nº1 (2000), 75-83.
 
 

24. Solutions to equations of p-Laplacian type in Lorentz spaces.

P. De Nápoli and M.C.Mariani.

Bulletin of The Belgian Mathematical Society 8 (2001), 469-477.
 
 
 

25. A Fixed Point Operator for a Nonlinear Boundary Value Problem.

P.Amster,  M.C.Mariani.

Journal of Mathematical Analysis and Applications 266 (2002), 160-168.
 
 

26. Local Existence of Solutions to the Transient Quantum Hydrodynamic Equations.

A. Jüngel, M.  C. Mariani, D. F. Rial.

To appear in Mathematical Models and Methods in Applied Science, M3AS.
 
 

27. Multiple solutions of a stationary nonhomogeneous nonlinear Schrodinger equation.

P. Amster, J. P. Borgna, M.  C. Mariani, D. F. Rial.

To appear in  Revista de la Unión Matemática Argentina.
 
 

28. The prescribed mean curvature equation for nonparametric surfaces.

P. Amster,  M.  C. Mariani.

To appear in Nonlinear Analysis.
 
 

29. A second order ODE with a nonlinear final condition.

P. Amster, M.  C. Mariani.

Electronic Journal of Differencial Equations 2001, 75, 1-9.
 
 

30.  Quasilinear elliptic systems of resonant type and nonlinear eigenvalue problems.

P. De Napoli, M. C. Mariani.

Abstract and Applied Analysis 7:3 (2002) 155-167.
 

31. Nonlinear periodic-type conditions for a second order  ODE

P. Amster, M. C. Mariani, D.Pinasco.

Nonlinear Studies, Vol. 8, 2, 2001.
 
 

32. Existence of solutions for elliptic systems with critical Sobolev exponent.

P. Amster, P. De Napoli, M. C. Mariani.

Electronic Journal of Differential Equations Vol. 2002 (2002) 49, 1-13.

33. Mountain Pass Solutions to Equations of p-Laplacian type.

P. De Nápoli, M.C. Mariani

To appear in Nonlinear Analysis.

34. Equations of p-Laplacian Type in Unbounded Domains.

P. De Nápoli, M.C. Mariani

To appear in Advanced Nonlinear Studies.
 

35. Solutions to a stationary nonlinear Black-Scholes type equation.

P. Amster, C. G. Averbuj and M. C. Mariani

To appear in Journal of Mathematical Analysis and Applications.

 36. Large Convergent Iterative Schemes for a Non-isentropic Hydrodynamic Model for Semiconductors.

P. Amster and R. Pinnau.

To appear in ZAMM.

Introducción a finanzas (2^nd Semester 1999 and 1st Semester 2002)
 

Matemática financiera (1st Semester 2000 and 1st Semester 2001)
 

Cálculo de Variaciones y Aplicaciones a Modelos Económicos

(1st Semester 2000)
 
 
The following program of the Maestría en Matemática Financiera (Master in Math Finance) has been aproved by the CODEP (Math Department Committee, Faculty of Physical and Natural Sciences, University of Buenos Aires) and the Faculty Committee, (Faculty of Physical and Natural Sciences, University of Buenos Aires).
 

Main courses:
   

• Introducción a finanzas

• Matemática financiera I

• Matemática financiera II

• Elementos de análisis y optimización

• Optimización e investigación operativa aplicados a Finanzas

• Herramientas para análisis de marketing estratégico

• Auditoría interna y operativa

• Matemática numérica aplicada a Finanzas

• Banca, seguros y finanzas

• Teoria de la predicción

Departamento de Física, Facultad de Ciencias Exactas y Naturales,

Universidad de Buenos Aires.
 
 

Prof. Angel Marzocca

Departamento de Física, Facultad de Ciencias Exactas y Naturales,

Universidad de Buenos Aires.
 
 
 
 

Prof. Irene Gamba

University of Texas at Austin
 
 

Prof. Ansgar Jüngel

Konstanz Universität, Germany
 
 

Courant Institute of Mathematical Sciences, New York University.

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