Research

Articles in Journals

  1.   Generic uniqueness and conjugate points for optimal control problems, (with A. Bressan and M. Mazzola), submitted.

  2.   A sharp quantitative estimate of critical sets, (with Andrew Murdza), submitted.

  3.   Hausdroff measure of zeros of polynomials, (with Andrew Murdza and E. Phillips), submitted.

  4.   Generic solutions to controlled balance laws , (with A. Bressan), submitted

  5.   On the structure of the value function of optimal exit time problems, (with P. Cannarsa and M. Mazzola), Calc. Var. Partial Differential Equations.

  6.   Piecewise regular solutions to scalar balance laws with singular source terms, (with L. Bociu, E. Ftaka and J. Schino), Journal of Differential Equations 409 (2004), 181-222.

  7.   Generic Properties of Conjugate Points in Optimal Control Problems, (with A. Bressan and M. Mazzola), Mathematical Control and Related Fields (2024)

  8.   Diffusion Approximations of Markovian Solutions to Discontinuous ODEs, (with Alberto Bressan and Marco Mazzola), Journal of Dynamical and Differential Equations 36 (2024), 1367--1404.

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

  10.   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.

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

  12.   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.

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

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

  15.   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.

  16.   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.

  17.   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.

  18.   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..

  19.   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.

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

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

  22.   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.

  23.   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.

  24.   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.

  25.   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.

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

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

  28.   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.

  29.   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.

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

  31.   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.

  32.   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.

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

  34.   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.

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

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

  37.   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.

  38.   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.

  39.   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

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

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

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

  43.  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.

  44.   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.

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

  46.   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.

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

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

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

  50.  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.

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

Proceedings

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

  2.   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.

  3.   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.

PhD thesis: The regularity of the minimum time function via nonsmooth analysis and geometric measure theory.

Recent collaborators : Fabio Ancona , E. N. Barron , Stefano Bianchini , Alberto Bressan , Piermarco Cannarsa , Giovanni Colombo , Antonio Marigonda , Marco Mazzola , Katrin Grunert, Michele Palladino , Davide Vittone , Olivier Glass
.