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List of Papers and Lectures
- Balance between degenerate elliptic operators and coercive Hamiltonians. arXiv:2608.02198 [math.AP] August, 2026. Preprint.New
- Fully nonlinear elliptic PDEs in thin domains with oblique-Dirichlet mixed boundary conditions.
Discrete Contin. Dyn. Syst. 57(2026),571-590.
- The vanishing discount problem for nonlocal Hamilton-Jacobi equations. arXiv:2504.11789 [math.AP] Nonlinear Anal. 274 (2027), Paper No. 114233.
- Fully nonlinear elliptic PDEs in thin domains with oblique boundary condition. arXiv:2410.23925 [math.AP] SIAM J. Math. Anal. 58 (2026), no. 2, 1232–1256.
- Liouville type results for the fractional truncated Laplacians in a half-space. arXiv:2501.08657 [math.AP] Nonlinearity 38 (2025), no. 6, Paper No. 065011, 39 pp.
- Test function approach to fully nonlinear equations in thin domains. arXiv:2404.19577 [math.AP] Proc. Amer. Math. Soc. 153 (2025), no. 5, 2099–2113.
- Propagation of minima for nonlocal operators. arXiv:2208.08164 [math.AP] Proc. Roy. Soc. Edinburgh Sect. A 154 (2024), no. 4, 1033-1046.
- The vanishing discount problem for monotone systems of Hamilton-Jacobi equations: a counterexample to the full convergence. arXiv:2202.02507 [math.AP] Math. Eng. 5 (2023), no. 4, Paper No. 072
- Nonlinear Neumann problems for fully nonlinear elliptic PDEs on a quadrant. arXiv:2108.13107 [math.AP] SIAM J. Math. Anal. 54 (2022), no. 6, 5854-5887
- Existence of an optimal path in a continuous-time nonconcave Ramsey model. Pure Appl. Funct. Anal. 7 (2022), no. 6, 1939-1952
- Hamilton-Jacobi equations with their Hamiltonians depending Lipschitz continuously on the unknown. arXiv:2108.11216 [math.AP] Comm. in Partial Differential Equations 47 (2022), no. 2, 417-452
- Discrete approximation of the viscous HJ equation. arXiv:2002.06674 [math.AP] Stoch. Partial Differ. Equ. Anal. Comput. 9 (2021), no. 4, 1081-1104.
- Existence and uniqueness of viscosity solutions of an integro-differential equation arising in option pricing. SIAM J. Financial Math. 12 (2021), no. 2, 604-640.
- Averaging of Hamilton-Jacobi equations over Hamiltonian flows. arXiv:1912.09153 [math.AP] Discrete Contin. Dyn. Syst. 41 (2021), no. 4, 1519-1542
- Positivity sets of supersolutions of degenerate elliptic equations and the strong maximum principle. arXiv:1911.08204 [math.AP] Trans. Amer. Math. Soc. 374 (2021), no. 1, 539-564
- The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. Part 1: linear coupling.
arXiv:1903.00244 [math.AP] Math. Eng. 3 (2021), no. 4, Paper No. 032, 21 pp.
- An example in the vanishing discount problem for monotone systems of Hamilton-Jacobi equations. arXiv:2006.02769 [math.AP] June, 2020.
- The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. Part 2: nonlinear coupling. arXiv:1906.07979 [math.AP] Calc. Var. Partial Differential Equations 59 (2020), no. 4, Paper No. 140, 28 pp.
- The vanishing discount problem for Hamilton-Jacobi equations in the Euclidean space. arXiv:1908.00869 [math.AP] Comm. Partial Differential Equations 45 (2020), no. 6, 525–560.
- Existence through convexity for the truncated Laplacians. arXiv:1902.08822 [math.AP]Math. Ann. 379 (2021), no. 3-4, 909–950.
- Vanishing contact structure problem and convergence of the viscosity solutions.arXiv:1808.06046 [math.AP] Comm. Partial Differential Equations 44 (2019), no. 9, 801–836..
- Towards a reversed Faber-Krahn inequality for the truncated Laplacian. arXiv:1803.07362 [math.AP] Rev. Mat. Iberoam. 36 (2020), no. 3, 723–740.
- A family of degenerate elliptic operators: maximum principle and its consequences. arXiv:1612.01700 [math.AP] Ann. Inst. H. Poincare Anal. Non Lineaire 35 (2018), no. 2, 417-441.
- On the Langevin equation with variable friction.
arXiv:1705.05478 [math.AP] Calc. Var. Partial Differential Equations 56 (2017), no. 6, Art. 161.
- The vanishing discount problem and viscosity Mather measures. Part 2: boundary value problems. arXiv:1607.04709 [math.AP] J. Math. Pures Appl. (9) 108 (2017), no. 3, 261-305.
- The vanishing discount problem and viscosity Mather measures. Part 1: the problem on a torus. arXiv:1603.01051 [math.AP] J. Math. Pures Appl. (9) 108 (2017), no. 2, 125-149.
- On viscosity solution of HJB equations with state constraints and reflection control. arXiv:1509.01118 [math.OC] SIAM J. Control Optim. 55 (2017), no. 1, 365–396.
- Metastability for parabolic equations with drift: part II. The quasilinear case. arXiv:1505.02265 [math.AP] Indiana Univ. Math. J. 66 (2017), no. 1, 315–360.
- Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, II. Bull. Math. Sci. 5 (2015), no. 3, 451–510.
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- A convergence result for the ergodic problem for Hamilton-Jacobi equations with Neumann type boundary conditions. Proc. Roy. Soc. Edinburgh Sect. A 146 (2016), no. 2, 225–242.PDF
- Metastability for parabolic equations with drift: part I. arXiv:1312.5504 [math.AP] Indiana Univ. Math. J. 64 (2015), no. 3, 875–913.
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- Asymptotic analysis for the eikonal equation with the dynamical boundary conditions. Math. Nachr. 287 (2014), no. 14-15, 1563–1588.PDF
- A new PDE approach to the large time asymptotics of solutions of Hamilton-Jacobi equations. arXiv:1210.7220 [math.AP]Bull. Math. Sci. 3 (2013), no. 3, 363–388.
- On the large time behavior of solutions of Hamilton-Jacobi equations associated with nonlinear boundary conditions. arXiv:1109.2762 [math.AP] Arch. Ration. Mech. Anal. 204 (2012), no. 2, 515–558.
- Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls. Ann. Inst. H. Poincaré C Anal. Non Linéaire 29 (2012), no. 5, 783–812. PDF
- A pde approach to small stochastic perturbations of Hamiltonian flows. J. Differential Equations 252 (2012), no. 2, 1748–1775. PDF
- Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions. arXiv:1008.4028 [math.AP] Calc. Var. Partial Differential Equations, 2011.
- Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions. arXiv:0910.0390 [math.AP] J. Math. Pures Appl. (9), 2011.
- A class of integral equations and approximation of p-Laplace equations. Calc. Var. Partial Differential Equations 37 (2010), no. 3-4, 485–522.PDF
- Non-local Hamilton-Jacobi equations arising in dislocation dynamics.Z. Anal. Anwend. 29 (2010), no. 3, 309–350. PDF
- Two remarks on periodic solutions of Hamilton-Jacobi equations. Recent progress on reaction-diffusion systems and viscosity solutions, 97–119.World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2009. PDF
- Correction: SDEs with oblique reflections on nonsmooth domains. arXiv:0809.4393 [math.PR] Annals of Probability 2008, Vol. 36, No. 5, 1992-1997
- Asymptotic solutions of Hamilton-Jacobi equations for large time and related topics.ICIAM 07—6th International Congress on Industrial and Applied Mathematics, 193–217.
European Mathematical Society (EMS), Zürich, 2009. PDF
- Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians.Arch. Ration. Mech. Anal. 194 (2009), no. 2, 383–419. PDF
- The large-time behavior of solutions of Hamilton-Jacobi equations on the real line. Methods Appl. Anal. 15 (2008), no. 2, 223–242. PDF
- Asymptotic solutions for large-time of Hamilton-Jacobi equations in euclidean n space. RIMS Kokyuroku,December, 2006. PDF
- Asymptotic solutions of Hamilton-Jacobi equations with semi-periodic Hamiltonians. Comm. Partial Differential Equations 33 (2008), no. 4-6, 784–807. PDF
- Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians. Indiana Univ. Math. J. 56 (2007), no. 5, 2159–2183. PDF
- Lecture at ICM 2006 Madrid. PDF
- Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean n space. International Congress of Mathematicians. Vol. III, 213–227. European Mathematical Society (EMS), Zürich, 2006.
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- Asymptotic solutions of Hamilton-Jacobi equations in Euclidean n space.Indiana Univ. Math. J. 55 (2006), no. 5, 1671–1700.PDF
- Asymptotic solutions of viscous Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator. Comm. Partial Differential Equations 31 (2006), no. 4-6, 827–848. PDF
- Limits of solutions of p-Laplace equations as p goes to infinity and related variational problems SIAM J. Math. Anal. 37 (2005), no. 2, 411–437. PDF
- Convexified Gauss curvature flow of bounded open sets in an anisotropic external field: a stochastic approximation and PDE. SIAM J. Math. Anal. 36 (2004), no. 2, 552–579. PDF
- Relaxation of Hamilton-Jacobi eqations. Arch. Ration. Mech. Anal. 169 (2003), no. 4, 265–304. PDF
- Asymptotic analysis for a class of infinite systems of first-order PDE. Comm. Partial Differential Equations 28 (2003), no. 1-2, 409–438. PDF
- A level set approach to the wearing process of a nonconvex stone. Calc. Var. Partial Differential Equations 19 (2004), no. 1, 53–93. PDF
- Relaxation in an L^\infty optimization problem. Proc. Roy. Soc. Edinburgh Sect. A 133 (2003), no. 3, 599–615. PDF
- Motion of a graph by R-curvature. Arch. Ration. Mech. Anal. 171 (2004), no. 1, 1–23. PDF
- Simultaneous effects of homogenization and vanishing viscosity in fully nonlinear elliptic equations. Funkcial. Ekvac. 46 (2003), no. 1, 63–88. PDF
- Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain. Nonlinear Anal. 57 (2004), no. 7-8, 1077–1098. PDF
- A class of stochastic optimal control problems with state constraint: an extended version. July, 2001 PDF
- A mathematical model of the wearing process of a nonconvex stone. SIAM J. Math. Anal. 33 (2001), no. 4, 860–876.
- A class of stochastic optimal control problems with state constraint. Indiana Univ. Math. J. 51 (2002), no. 5, 1167–1196. PDF
- On ε-optimal controls for state constraint problems. Ann. Inst. H. Poincaré C Anal. Non Linéaire 17 (2000), no. 4, 473–502.PDF
- Almost periodic homogenization of Hamilton-Jacobi equations. International Conference on Differential Equations, Vol. 1, 2 (Berlin, 1999), 600–605.PDF
- A PDE approach to state-constraint problems in Hilbert spaces.July 14, 1999. PDF
- User's guide to viscosity solutions of second order partial differential equations.
arXiv:math/9207212 [math.AP] Bull. Amer. Math. Soc. (N.S.) 27 (1992) 1-67
- Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets. Bull. Fac. Sci. Engrg. Chuo Univ. 1985. PDF
- Remarks on Existence of Viscosity Solutions of Hamilton-Jacobi Equations. Bull. Fac. Sci. Engrg. Chuo Univ.1983.PDF
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