• Balance between degenerate elliptic operators and coercive Hamiltonians. 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. Nonlinear Anal. 274 (2027), Paper No. 114233.
• Fully nonlinear elliptic PDEs in thin domains with oblique boundary condition. SIAM J. Math. Anal. 58 (2026), no. 2, 1232–1256.
• Liouville type results for the fractional truncated Laplacians in a half-space. Nonlinearity 38 (2025), no. 6, Paper No. 065011, 39 pp.
• Test function approach to fully nonlinear equations in thin domains. Proc. Amer. Math. Soc. 153 (2025), no. 5, 2099–2113.
• Propagation of minima for nonlocal operators. 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. Math. Eng. 5 (2023), no. 4, Paper No. 072
• Nonlinear Neumann problems for fully nonlinear elliptic PDEs on a quadrant. 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. Comm. in Partial Differential Equations 47 (2022), no. 2, 417-452
• Discrete approximation of the viscous HJ equation. 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. Discrete Contin. Dyn. Syst. 41 (2021), no. 4, 1519-1542
• Positivity sets of supersolutions of degenerate elliptic equations and the strong maximum principle. 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. 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. June, 2020.
• The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. Part 2: nonlinear coupling. 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. August, 2019; Comm. in PDE.
• Existence through convexity for the truncated Laplacians. February, 2019; Math. Ann.
• Vanishing contact structure problem and convergence of the viscosity solutions. August, 2018; Comm in PDE.
• Towards a reversed Faber-Krahn inequality for the truncated Laplacian. March, 2018; Rev. Mat. Iberoam.
• A family of degenerate elliptic operators: maximum principle and its consequences. Ann. Inst. H. Poincare Anal. Non Lineaire 35 (2018), no. 2, 417-441.
• On the Langevin equation with variable friction Calc. Var. Partial Differential Equations 56 (2017), no. 6, Art. 161.
• The vanishing discount problem and viscosity Mather measures. Part 2: boundary value problems. 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. J. Math. Pures Appl. (9) 108 (2017), no. 2, 125-149.
• On viscosity solution of HJB equations with state constraints and reflection control, Sept, 2015
• Metastability for parabolic equations with drift: part II. The quasilinear case, May, 2015; Indiana Univ. Math. J.
• Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, II (Oct, 2014) Bull. Math. Sciences
• A convergence result for the ergodic problem for Hamilton-Jacobi equations with Neumann type boundary conditions Oct, 2014
• Metastability for parabolic equations with drift: part 1, Dec, 2013 (revision: June, 2014)
• Asymptotic analysis for the eikonal equation with the dynamical boundary conditions, Aug, 2013
• A new PDE approach to the large time asymptotics of solutions of Hamilton-Jacobi equations, Oct, 2012
• On the large time behavior of solutions of Hamilton-Jacobi equations associated with nonlinear boundary conditions, Sept, 2011
• Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, August, 2011 PDF (358Kb)
• A pde approach to small stochastic perturbations of Hamiltonian flows, May, 2011 PDF (295Kb)
• Long-time asymptotic solutions of convex Hamilton-Jacobi equations with Neumann type boundary conditions, August, 2010
• Weak KAM aspects of convex Hamilton-Jacobi equations with Neumann type boundary conditions (arXiv:0910.0390), October, 2009 PDF (402Kb)
• A class of integral equations and approximation of p-Laplace equations, July, 2009. PDF (319Kb)
• Non-local Hamilton-Jacobi equations arising in dislocation dynamics, January, 2009 PDF (305Kb)
• Two remarks on periodic solutions of Hamilton-Jacobi equations, October, 2008 PDF (255Kb)
• Correction: SDEs with oblique reflections on nonsmooth domains, 2008 PDF (77Kb)
• Asymptotic solutions of Hamilton-Jacobi equations for large time and related topics March, 2008 PDF (412Kb)
• Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians, March, 2008 PDF (279Kb)
• The large-time behavior of solutions of Hamilton-Jacobi equations on the real line. March, 2008 PDF (203Kb)
• Asymptotic solutions for large-time of Hamilton-Jacobi equations in euclidean n space. December, 2006 PDF (189Kb)
• Asymptotic solutions of Hamilton-Jacobi equations with semi-periodic Hamiltonians. January, 2007 PDF (240Kb)
• Lecture at ICM2006Madrid September, 2006 PDF (168Kb)
• Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians February, 2007 PDF (198Kb)
• Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean n space August, 2006 PDF (289Kb) Original PDF (315Kb)
• Asymptotic solutions of Hamilton-Jacobi equations in Euclidean n space June, 2005 PDF (178Kb)
• Asymptotic solutions of viscous Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator January, 2005 PDF (275Kb)
• Limits of solutions of p-Laplace equations as p goes to infinity and related variational problems January, 2005 PDF (295Kb)
• Convexified Gauss curvature flow of bounded open sets in an anisotropic external field: a stochastic approximation and PDE November, 2002 PDF (335Kb)
• Relaxation of Hamilton-Jacobi eqations October, 2002 PDF (248Kb)
• Asymptotic analysis for a class of infinite systems of first-order PDE, April, 2002 PDF (276Kb)
• A level set approach to the wearing process of a nonconvex stone. October, 2002 PDF (437Kb)
コードは注意してご使用ください。Relaxation in an L^infty optimization problem. November, 2001 PDF (198Kb)Motion of a graph by R-curvature. October, 2001 PDF (240Kb)Simultaneous effects of homogenization and vanishing viscosity in fully nonlinear elliptic equations. October, 2001 PDF (231Kb)Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain. September, 2001A Class of Stochastic Optimal Control Problems with State Constraint: An Extended Version. July, 2001 PDF (361Kb)A Mathematical Model of the Wearing Process of a Nonconvex Stone. March, 2001A Class of Stochastic Optimal Control Problems with State Constraint. July, 2000 PDF (206Kb)On ε-optimal controls for state constraint problems August 7, 1999;Almost periodic homogenization of Hamilton-Jacobi equations July 29, 1999;A PDE approach to state-constraint problems in Hilbert spaces July 14, 1999;User's guide to viscosity solutions of second order partial differential equations, Bulletin of AMS, 1992. (Reprints)Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets. Bull. Fac. Sci. Engrg. Chuo Univ. 1985.Remarks on Existence of Viscosity Solutions of Hamilton-Jacobi Equations. Bull. Fac. Sci. Engrg. Chuo Univ. 1985.← Back to Home