Research

Articles in Journals

•   On the structure of the value function of optimal exit time problems, (with P. Cannarsa and M. Mazzola), submitted.

•   Generic Properties of Conjugate Points in Optimal Control Problems, (with A. Bressan and M. Mazzola), submitted.

•   Zeros of polynomials and critical sets, (with Andrew Murdza and E. Phillips), submitted.

•   Piecewise regular solutions to scalar balance laws with singular source terms, (with L. Bociu, E. Ftaka and J. Schino), submitted.

•   Diffusion Approximations of Markovian Solutions to Discontinuous ODEs, (with Alberto Bressan and Marco Mazzola), Journal of Dynamics and Differential Equations (2024).

•   A debt management problem with currency devaluation, (with Antonio Marigonda), Mathematical Control and Related Fields 14 (2024), 513-532.

•   Examples and conjectures on the regularity of solutions to balance laws, (with Ancona F., Bianchini S., Bressan A., and Colombo R.;), Quarterly of Applied Mathematics 81 (2023), no.3, 433-454.

•   Generic Properties of First Order Mean Field Games, (with Alberto Bressan), Dynamic Games and Applications 13 (2023), no. 3, 750-782.

•   A lower bound on the quantitative version of the transversality theorem, (with Andrew Murdza), Journal of Mathematical Analysis and Applications 528 (2023), no. 1, Paper No. 127539.

•   A quantitative version of the transversality theorem, (with Andrew Murdza), Communications in Mathematical Sciences 21 (2023), no. 5 1302-1320.

•   Generalized Differential Games , (with E.N. Barron), Dynamic Games and Applications (DGAA) 13(2023), no. 3, 705-720.

•   Shock interactions for the Burgers-Hilbert Equation , (with A. Bressan, S.T. Galtung, and K. Grunert), Communications in Partial Differential Equations 47 (2022), no. 2, 1795-1844.

•   Metric entropy for Hamilton-Jacobi equation with uniformly directionally convex Hamiltonian, (with Stefano Bianchini and Prerona Dutta), SIAM Journal on Mathematical Analysis 54 (2022), 5551-5575.

•   Solutions to a system of first order H-J equations related to a debt management problem, (with Antonio Marigonda), NoDEA Nonlinear Differential Equations Appl. 29(2022), no. 4, 34 pages.

•   On the global controllability of scalar conservation laws with boundary and source controls, (with Fabio Ancona), SIAM Journal on Control and Optimization 59 (2021), no. 6, 4314--4338..

•   Metric entropy for functions of bounded total generalized variation, (with Rossana Capuani and Prerona Dutta), SIAM Journal on Mathematical Analysis 53 (2021), no. 1, 1168--1190.

•   Markovian solutions to discontinuous ODEs, (with Alberto Bressan and Marco Mazzola), Journal of Dynamical and Differential Equations (2021).

•   SBV regularity for Burgers-Poisson equation, (with Steven Gilmore), Journal of Mathematical Analysis and Applications, 500 (2021), no. 1.

•   A model of debt with bankruptcy risk and currency devaluation, (with Rossana Capuani and Steven Glimore), Minimax Theory and its Applications , 5 (2020), no. 2, 23 pp.

•   Lyapunov's theorem via Baire category, (with Marco Mazzola), Trends in control theory and partial differential equations, 181--194, Springer INdAM Series, 32, Springer, Cham, 2019.

•   On Kolmogorov entropy compactness estimates for scalar conservation laws without uniform convexity , (with Fabio Ancona and Olivier Glass), SIAM Journal on Mathematical Analysis , 51 (2019), no. 4, 3020--3051.

•   Approximation of sweeping processes and controllability for a set valued evolution , (with Alberto Bressan and Marco Mazzola), SIAM Journal on Control and Optimization 57 (2019), no. 4, 2487--2514.

•   Covering numbers for bounded variation functions, (with Prerona Dutta), Journal of Mathematical Analysis and Applications 468 (2018), no. 2, 1131--1143.

•   Stability of feedback solutions for infinite horizon noncooperative differential games, (with Alberto Bressan), Dynamic Games and Applications (DGAA) 8 (2018), no. 1, 42--78.

•   Generalized control systems in the space of probability measures, (with Giulia Cavagnari, Antonio Marigonda, Fabio S. Priuli), Set-Valued and Variational Analysis 26 (2018), no. 3, 663--691.

•   A stochastic model of optimal debt management and bankruptcy, (with Alberto Bressan, Antonio Marigonda, Michele Palladino), SIAM Journal on Financial Mathematics 8 (2017), 841--873.

•   On the Burgers-Poisson equation, (with Katrin Grunert), Journal of Differential Equations 23 (2016), 3220--3246.

•   The compactness estimates for Hamilton Jacobi Equations depending on space, (with Fabio Ancona and Piermarco Cannarsa), Bulletin of the Institute of Mathematics, Academia Sinica 11 (2016), 63--114.

•   Quantitative compactness estimates for Hamilton-Jacobi equations, (with Fabio Ancona and Piermarco Cannarsa), Archive for Rational Mechanics and Analysis 219 (2016), no. 2, 793--828.

•   An equilibrium model of debt and bankruptcy, (with Alberto Bressan), ESAIM: Control, Optimisation and Calculus of Variations , 22 (2016), no. 4, 953--982.

•   The Bang-Bang theorem via Baire category. A Dual Approach , (with Alberto Bressan, Marco Mazzola), NoDEA Nonlinear Differential Equations Appl. 23 (2016), no. 4, 23--46.

•   Optima and Equilibria for Traffic Flow on Networks with Backward Propagating Queues, (with Alberto Bressan), Networks & Heter. Media 10 (2015), no. 4, 717--748.

•   Conservation law models for traffic flow on a network of roads, (with Alberto Bressan), Networks & Heter. Media 10 (2015), no. 2, 255--292.

•   On lower compactness estimates for general nonlinear hyperbolic systems, (with Fabio Ancona and Oliver Glass), Ann. Inst. H. Poincare Anal. Non Lineaire 6 (2015), 1229--1257.

•   Optimality conditions and regularity results for time optimal control problems with differential inclusions, (with Piermarco Cannarsa and Antonio Marigonda), Journal of Mathematical Analysis and Applications 427 (2015), no. 1, 202--228.

•   Non-Lipschitz points and the SBV regularity of the minimum time function, (with Giovanni Colombo, Luong V. Nguyen), Calc. Var. Partial Differential Equations 51 (2014), no .1-2, 439--463

•   Global existence of weak solutions for the Burgers-Hilbert equation, (with Alberto Bressan), SIAM Journal on Mathematical Analysis 46 (2014), no. 4, 2884--2904.

•   Singular gradient flow and homotopic equivalence, (with P. Albano, P. Cannarsa and C. Sinestrari), Mathematische Annalen 356 (2013), 23--43.

•   The minimum time function around the origin, (with Giovanni Colombo), Mathematical Control and Related Fields 3 (2013), no. 1, 51--82.

•  Some regularity results for a class of upper semicontinuous functions, (with Antonio Marigonda and Davide Vittone), Indiana University Mathematics Journal 62 (2013) no. 1, 45--90.

•   Lower compactness estimates for scalar balance laws, (with Fabio Ancona and Olivier Glass), Communications on Pure and Applied Mathematics 65 (2012), no. 9, 1303--1329.

•   Rectifiability of special singularities of non-lipschitz functions, (with Davide Vittone), Journal of Convex Analysis 19 (2012), no. 1, 159--170.

•   External sphere condition and time optimal control for differential inclusions, (with Piermarco Cannarsa), SIAM Journal on Control and Optimization 49 (2011), no. 6, 2558--2576.

•   On the structure of the minimum time function, (with Giovanni Colombo), SIAM Journal on Control and Optimization 48 (2010), no. 7, 4776--4814.

•  Hypographs satisfying external sphere condition and the regularity of the minimum time function, Journal of Mathematical Analysis and Applications 372 (2010), 611--628.

•   Quantitative isoperimetric inequalities for a class of nonconvex sets, (with Giovanni Colombo), Calc. Var. Partial Differential Equations 37 (2010), no. 1-2, 141--166.

•  Morse-Palais Lemma for nonsmooth functionals on normed spaces (with Duong Minh Duc, Tran Vinh Hung), Proc. Amer. Math. Soc. 135 (2007), no. 3, 921--927.

•  Critical points of non-C2 functional (with Duong Minh Duc, Tran Vinh Hung), Topol. Methods Nonlinear Anal. 29 (2007), no. 1, 35--68.

Proceedings

•   Quantitative compactness estimate for scalar conservation laws with nonconvex fluxes , (with Fabio Ancona and Olivier Glass), Proceeding of Hyp2018 .

•   BV regularity and differentiability properties of a class of upper semicontinuous functions, (with Antonio Marigonda and Davide Vittone), The Ninth International Conference on "Large Scale Scientific Computations", June 3-7, 2013, Sozopol, Bulgaria.

•   On quantitative compactness for hyperbolic conservation laws, (with Fabio Ancona and Olivier Glass), Hyperbolic problems: theory, numerics and applications. Proceedings of the 14th International Conference on Hyperbolic Problems (HYP2012), AIMS, Springfield, MO, 2014.