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Journal of Functional Analysis, ISSN 0022-1236, 10/2018, Volume 275, Issue 8, pp. 2096 - 2161
We propose notions of minimax and viscosity solutions for a class of fully nonlinear path-dependent PDEs with nonlinear, monotone, and coercive operators on... 
Nonlinear evolution equations | Path-dependent PDEs | Minimax solutions | Optimal control | BOUNDARY CONTROL-PROBLEMS | HJB EQUATIONS | VISCOSITY SOLUTIONS | STATE CONSTRAINTS | NONLINEAR 2ND-ORDER EQUATIONS | MATHEMATICS | RISK-SENSITIVE CONTROL | PARTIAL-DIFFERENTIAL-EQUATIONS | BELLMAN EQUATIONS | OPTIMAL STOCHASTIC-CONTROL | SADDLE-POINT
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 09/2016, Volume 261, Issue 5, pp. 2702 - 2737
We prove stochastic homogenization for a general class of coercive, nonconvex Hamilton–Jacobi equations in one space dimension. Some properties of the... 
Nonconvex Hamilton–Jacobi equation | Dynamical properties of effective Hamiltonians | Metric problem | Stochastic homogenization | Nonconvex Hamilton-Jacobi equation | MATHEMATICS | BELLMAN EQUATIONS | MEDIA | Analysis of PDEs | Mathematics
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2018, Volume 40, Issue 2, pp. A629 - A652
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 6/2013, Volume 20, Issue 3, pp. 413 - 445
We consider continuous-state and continuous-time control problems where the admissible trajectories of the system are constrained to remain on a network. In... 
Networks | Secondary 34H05 | 35F21 | Analysis | Optimal control | Graphs | Mathematics | Hamilton–Jacobi equations | Primary 35R02 | 35Q93 | 49J15 | Viscosity solutions | Hamilton-Jacobi equations | MATHEMATICS, APPLIED | STATE CONSTRAINTS | BELLMAN EQUATIONS | Analysis of PDEs
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 12/2017, Volume 263, Issue 12, pp. 8418 - 8466
This paper studies optimal control problems on networks without controllability assumptions at the junctions. The Value Function associated with the control... 
Stratified structure | Hamilton–Jacobi equations | State constraint problems | Control problem on networks | MATHEMATICS | Hamilton-Jacobi equations | R-N | BELLMAN APPROACH | EIKONAL EQUATIONS | Analysis of PDEs | Mathematics | Optimization and Control
Journal Article
Applied Mathematics and Optimization, ISSN 0095-4616, 06/2018, Volume 77, Issue 3, pp. 599 - 611
Journal Article
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, ISSN 0363-0129, 2019, Volume 57, Issue 1, pp. 23 - 52
In this paper we study the ergodic problem for viscous Hamilton-Jacobi equations with superlinear Hamiltonian and inward drift. We investigate (i) existence... 
MATHEMATICS, APPLIED | stochastic ergodic control | LARGE TIME BEHAVIOR | ergodic problem | generalized principal eigenvalue | BELLMAN EQUATIONS | viscous Hamilton-Jacobi equation | AUTOMATION & CONTROL SYSTEMS | Analysis of PDEs | Mathematics
Journal Article
International Journal of Control, ISSN 0020-7179, 10/2019, Volume 92, Issue 10, pp. 2263 - 2273
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 06/2017, Volume 127, Issue 6, pp. 1926 - 1959
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2016, Volume 38, Issue 3, pp. A1587 - A1615
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2017, Volume 55, Issue 2, pp. 691 - 712
Journal Article
Journal of Machine Learning Research, ISSN 1532-4435, 09/2018, Volume 19, pp. 1 - 49
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 02/2019, Volume 122, pp. 164 - 197
We consider a family of optimal control problems in the plane with dynamics and running costs possibly discontinuous across a two-scale oscillatory interface.... 
Homogenization | Discontinuous Hamiltonian | Hamilton–Jacobi equations | Effective transmission condition | Oscillatory interface | MATHEMATICS | Hamilton-Jacobi equations | MATHEMATICS, APPLIED | BELLMAN APPROACH | JUNCTION PROBLEMS | Numerical Analysis | Computer Science
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2015, Volume 37, Issue 1, pp. A181 - A200
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2017, Volume 456, Issue 2, pp. 1347 - 1364
In this paper, we concern the multidimensional viscosity solution theory of a kind of semi-linear partial differential equations (PDEs). A new definition of... 
BSDEs | Multidimensional PDEs | Comparison theorem | Viscosity solution | MATHEMATICS | JACOBI-BELLMAN EQUATIONS | MATHEMATICS, APPLIED | MONOTONE SYSTEMS | GAMES | PDES | UNIQUENESS | Differential equations
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