Home page of Hitoshi Ishii

Liouville type results for the fractional truncated Laplacians in a half-space. January, 2025. Preprint. New
Fully nonlinear elliptic PDEs in thin domains with oblique boundary condition. October, 2024. Preprint.
Test function approach to fully nonlinear equations in thin domains. April, 2024. Proc. AMS, to appear.
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.
An example in the vanishing discount problem for monotone systems of Hamilton-Jacobi equations . June, 2020.

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.

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.

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.

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.

On the Langevin equation with variable friction Calc. Var. Partial Differential Equations 56 (2017), no. 6, Art. 161.

A family of degenerate elliptic operators: maximum principle and its consequences. Ann. Inst. H. Poincare Anal. Non Lineaire 35 (2018), no. 2, 417-441.

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-download- pdf file (358Kb)

A pde approach to small stochastic perturbations of Hamiltonian flows, May, 2011-download- pdf file (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-download- pdf file (402Kb)

A class of integral equations and approximation of p-Laplace equations, July, 2009. The copyright has been transferred to Springer-Verlag, CVPDE; The original publication is available at www.springerlink.com-download- pdf file (319Kb)

Non-local Hamilton-Jacobi equations arising in dislocation dynamics, to appear in ZAA, January, 2009-download- pdf file (305Kb)

Two remarks on periodic solutions of Hamilton-Jacobi equations, October, 2008-download- pdf file (255Kb)

Correction: SDEs with oblique reflections on nonsmooth domains The Annals of Probability 21 (1993) 554-580 Ann. Prob. 36(2008) no. 5, 1992-1997-download- pdf file (77Kb)

Asymptotic solutions of Hamilton-Jacobi equations for large time and related topics March, 2008- download- pdf file (412Kb)

Long-time behavior of solutions of Hamilton-Jacobi equations with convex and coercive Hamiltonians (Arch. Rat. Mech. Anal., to appear) The original publication is available at www.springerlink.com March, 2008- download- pdf file (279Kb)

The large-time behavior of solutions of Hamilton-Jacobi equations on the real line. (Methods Appl. Anal., to appear) March, 2008 -download- pdf file (203Kb)

Asymptotic solutions for large-time of Hamilton-Jacobi equations in euclidean n space. (for RIMS kokyuroku), December, 2006 -download- pdf file (189Kb)

Asymptotic solutions of Hamilton-Jacobi equations with semi-periodic Hamiltonians. January, 2007 (Comm. PDE, to appear) -download- pdf file (240Kb)

Lecture at ICM2006Madrid September, 2006 -download- pdf file (168Kb)

Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians February, 2007 (Indiana Univ. Math. J., 56(2007), no. 3, pp. 2159-2184). Formerly: Representation formulas for solutions of Hamilton-Jacobi equations June, 2006 -download- pdf file (198Kb)

Asymptotic solutions for large time of Hamilton-Jacobi equations in Euclidean n space August, 2006 (Annales de l'IHP-Analyse non lineaire, 25, issue 2, 2008, pp. 231-266) -download- Current version pdf file (289Kb) Original version (December, 2005) pdf file (315Kb)

Asymptotic solutions of Hamilton-Jacobi equations in Euclidean n space June, 2005 (Cpyright: Indiana Univ. Math. J., to appear) -download- pdf file (178Kb); gziped post script file (137Kb)

Asymptotic solutions of viscous Hamilton-Jacobi equations with Ornstein-Uhlenbeck operator January, 2005 (Copyright: Comm PDE 31(2006) no. 6) -download- pdf file (275Kb); gziped post script file (215Kb)

Limits of solutions of p-Laplace equations as p goes to infinity and related variational problems January, 2005 = revised version(Copyright: SIAM J. Math. Anal., to appear), March, 2004 (original version) -download- pdf file (295Kb); gziped post script file (242Kb)

Convexified Gauss curvature flow of bounded open sets in an anisotropic external field: a stochastic approximation and PDE November, 2002 -download- pdf file (335Kb); gziped post script file (227Kb)

Relaxation of Hamilton-Jacobi eqations October, 2002, Revised version March, 2003 (Copyright: Arch. Rat. Mech. Anal., to appear) -download- pdf file (248Kb) ;gziped post script file (222Kb)

Asymptotic analysis for a class of infinite systems of first-order PDE: nonlinear parabolic PDE in the singular limit. April, 2002 (Copyright: Marcel Dekker, Inc. (Comm. in PDE, vol. 28 (2003) http://www.dekker.com/servlet/product/productid/PDE)) -download- pdf file (276Kb); gziped post script file (204Kb)

A level set approach to the wearing process of a nonconvex stone. Revised version, October, 2002 (Copyright: Springer-Verlag (Calc. Var. PDEs), http://www.springerlink.com, June 6, 2003), originally: February, 2002 -download- pdf file (437Kb); gziped post script file (192Kb)

Relaxation in an $L^\infty$ optimization problem. November, 2001 Revised version. August, 2002 (Copyright: Proc. Royal Soc. Edinburgh, to appear) -download- pdf file (198Kb); gziped post script file (103Kb)

Motion of a grapf by R-curvature. October, 2001 -download- pdf file (240Kb); gziped post script file (130Kb)

Simultaneous effects of homogenization and vanishing viscosity in fully nonlinear elliptic equations. October, 2001 (to appear in Funk. Ekvac.) -download- pdf file (231Kb); gziped post script file (147Kb)

Nonlinear oblique derivative problems for singular degenerate parabolic equations on a general domain. September, 2001: Nonlinear Analysis, TMA

A Class of Stochastic Optimal Control Problems with State Constraint: An Extended Version. July, 2001 -download- pdf file (361Kb); gziped post script file (218Kb)

A Mathematical Model of the Wearing Process of a Nonconvex Stone. March, 2001: SIAM J. Math. Anal. 33 (2001), no. 4, 860 - 876. ERRATA

A Class of Stochastic Optimal Control Problems with State Constraint. July, 2000 (Copyright: Indiana Univ. Math. J., to appear) -download- pdf file (206Kb); gziped post script file (134Kb)

On $\varepsilon$-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; gziped post script file(88kb)

MEMO(4/26/11)

Reprints

User's guide to viscosity solutions of second order partial differential equations, Bulletin of AMS, 1992.

Hamilton-Jacobi equations with discontinuous Hamiltonians on arbitrary open sets. Bull. Fac. Sci. Engrg. Chuo Univ. 28 1985, 33--77.

Remarks on Existence of Viscosity Solutions of Hamilton-Jacobi Equations. Bull. Fac. Sci. Engrg. Chuo Univ. 26 1985, 5--24.

Curriculum Vitae

List of papers

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