Lecture Notes

Calculus of Variations
Distribution Theory (in Portuguese)
Introduction to Analysis (preliminary version available by request).
Introduction to Linear Optimization (preliminary version available by request), joint with A. Sernadas and C. Sernadas.

Publications

A-priori estimates for stationary mean-field games. With G. Pires and H. Sanchez- Morgado. To appear in Networked and Heterogeneous Media.
Convergence of a numerical scheme for the Hamilton-Jacobi equation: a new approach with the adjoint method. With F. Cagnetti e H. Tran. To appear in Aplied Numerical Analysis.
Wigner measures and the semi-classical limit to the Aubry-Mather measure With A. Lopes e J. Mohr. To appear App. Math. Research Express.
Systems of weakly coupled Hamilton-Jacobi equations with implicit obstacles. With A. Serra. Can. J. Math, doi:10.4153/CJM-2011-085-7, 2011.
Cagnetti, F.; Gomes, D.; Tran, H. V. Aubry-Mather measures in the nonconvex setting. SIAM J. Math. Anal. 43 (2011), no. 6, 2601–2629
The Mather measure and a Large Deviation Principle for the Entropy Penalized Method, with A. Lopes and J. Mohr. Commun. Contemp. Math. 13 (2011), no. 2, 235–268.
Biryuk, Andrey; Gomes, Diogo A. An introduction to the Aubry-Mather theory. São Paulo J. Math. Sci. 4 (2010), no. 1, 17–63.
Gomes, Diogo A.; Jung, Nara; Lopes, Artur O. Minimax probabilities for Aubry-Mather problems. Commun. Contemp. Math. 12 (2010), no. 5, 789–813.
Discrete time, finite state space mean field games, with J. Mohr and R. Souza. Journal de Mathématiques Pures et Appliquées, 93 (2010), pp. 308-328.
Viscosity solutions and converse KAM, with Adam Oberman. Vol 42 (2008), no 6, pp. 1047--1064.
Selection criteria for Hamilton-Jacobi equations and Aubry-Mather measures, Advances in Calculus of Variations, 1 (2008), no. 3, pp. 291-307.
An error estimate for the approximation of the effective Hamiltonian, with F. Camilli e I. Capuzzo Dolcetta, Applied Mathematics and Optimization, Vol. 57 (2008), no. 1, pp. 30--57.
Entropy penalization methods for Hamilton-Jacobi equations, with Enrico Valdinoci, Advances in Mathematics, Vol. 215 (2007), no. 1, 94--152.
Convergence of Viscosity Solutions of Burgers equations with Random Forcing, with R. Iturriaga, K. Khanin, and P. Padilla, Moscow Math. Journal, Vol. 5 (2005) no. 3.
Semiclassical limits and classical mechanics, with Claudia Valls, Asymptotic Analysis, Vol. 51 (2007) no. 1, pp. 47-62.
Weak KAM theory for multidimensional maps, with Claudia Valls, Mathematical Physics Electronic Journal, Vol. 12 (2006) no. 3.
Computing the Effective Hamiltonian using a Variational Approach, with Adam Oberman, to appear in proceedings of CDC-05.
Hamilton-Jacobi methods for Vakonomic Mechanics, to appear in NoDEA.
Viscosity solution methods and the discrete Aubry-Mather problem, accepted for publication at "Discrete and Continuous Dynamical Systems"
A variational principle for Navier Stokes equation, accepted for publication at Communications in Mathematical Physics.
Approximation of ill-posed Boussinesq equations, with C. Valls, accepted for publication at Dynamical Systems.
Duality principles for fully-nonlinear elliptic equations, accepted for publication in Progress in Nonlinear Differential Equations and Their Applications, Vol. 61, pp. 125-136.
Lack of integrability via viscosity solutions methods, with E. Valdinoci, accepted for publication at the Indiana University Mathematics Journal.
Computing the effective Hamiltonian - a variational approach to homogenization with Adam Oberman, accepted for publication at SIAM jornal of Control and Optimization.
Perturbation theory for Hamilton-Jacobi equations and stability of Aubry-Mather sets, accepted for publication in the SIAM journal of Mathematical Analysis.
Linear Programming Interpretations of Mather's Variational Principle - with L. C. Evans, Optimization and Calculus of Variations 8 (2002).
Effective Hamiltonians and Averaging for Hamiltonian Dynamics I - with L. C. Evans, Archives of Rational Mechanics and Analysis, 157, no. 1, 2001.
Effective Hamiltonians and Averaging for Hamiltonian Dynamics II - with L. C. Evans, Archives of Rational Mechanics and Analysis, 161 no. 4 (2002).
A Stochastic Analog of Aubry-Mather Theory - Nonlinearity 10, no. 3 (2002), pp. 271-305.
Regularity Theory for Hamilton-Jacobi Equations, Journal of Differential Equations 187 (no. 2) 2003.
Viscosity Solutions of Hamilton-Jacobi Equations, and Asymptotics for Hamiltonian Systems - Journal of Calculus of Variations and Partial Differential Equations, 14 (no. 3) 2002.
Stability of Rotating Liquid Films , Quarterly Journal of Mechanics and Applied Mathematics, 55 (no. 3) 2002. (some pictures can be downloaded separately Plateau-Rayleigh Instability , Toroidal configuration, Toroidal configuration (section), Asymmetric Instability ).
Chaotic Motions in Vortices Dynamics - in proceedings of Equadiff95, World Scientific.
Integrability/Non-Integrability in Vortices Dynamics - in Universitatis Iagellonicae Acta Mathematica, Fasciculus XXXVI, 1997.
A Symmetry Breaking Experiment Aboard Mir and the Stability of Rotating Liquid Films, with P. Concus, R. Finn, J. McCuan and M. Weislogel (also the abstract in PDF), Fourth Microgravity Fluid Physics and Transport Phenomena Conference

Lecture notes, Introductory Material, Thesis, etc

My Ph.D. thesis - Viscosity Solutions and Asymptotics for Hamiltonian Systems.
Linear Programming and Nonlinear Partial Differential Equations - a informal introductions to the heuristics of Aubry-Mather theory, Monge-Kantorowich problems.
Viscosity solutions and Aubry-Mather theory, Appendix to the book "Geometric Mechanics" by Waldyr Oliva.
Lecture Notes on Calculus of Variations - preliminary version (in Portuguese).
Theory of distributions - preliminary version (in Portuguese).

Conferences Slides

Viscosity solutions and integrability of Hamiltonian systems - "New connections between dynamical systems and PDEs", American Institute of Mathematics, Palo Alto, July 6-10, 2003.