Liouville-type theorems for fully nonlinear elliptic and parabolic equations with boundary degeneracy, (with E. Zhanpeisov), submitted for publication.
A parabolic PDE-based approach to Borell--Brascamp--Lieb inequality, (with K. Ishige and P. Salani), submitted for publication.
Horizontal semiconcavity for the square of Carnot-Caratheodory distance on step 2 Carnot groups and applications to Hamilton-Jacobi equations, (with F. Dragoni and Y. Zhang), submitted for publication.
A second-order operator for horizontal quasiconvexity in the Heisenberg group and application to convexity preserving for horizontal curvature flow, (with A. Kijowski, Y. Zhang and X. Zhou), submitted for publication.
Discontinuous eikonal equations in metric measure spaces, (with N. Shanmugalingam and X. Zhou), Trans. Amer. Math. Soc., 378 (2025), 695--729.
A representation formula for viscosity solutions of nonlocal Hamilton-Jacobi equations and applications, (with T. Kagaya and H. Mitake), SIAM J. Math. Anal., 56 (2024), 5807--5839.
Horizontally quasiconvex envelope in the Heisenberg group, (with A. Kijowski and X. Zhou), Rev. Mat. Iberoam., 40 (2024), 57--92.
Quasiconvexity presering property for fully nonlinear nonlocal parabolic equations, (with T. Kagaya and H. Mitake), NoDEA Nonlinear Differential Equations Appl., 30 (2023), Paper No. 13.
Differential games and Hamilton-Jacobi-Isaacs equations in metric spaces, (with X. Zhou), Minimax Theory Appl., 8 (2023), 121-138.
Principal eigenvalue problem for infinity Laplacian in metric spaces, (with A. Mitsuishi), Adv. Nonlinear Stud., 22 (2022), 548--573.
Singular Neumann boundary problems for a class of fully nonlinear parabolic equations in one dimension, (with T. Kagaya), SIAM J. Math. Anal., 53 (2021), 4350-4385.
Equivalence of solutions of eikonal equation in metric spaces, (with N. Shanmugalingam and X. Zhou), J. Differential Equations, 272 (2021), 979-1014.
A game-theoretic approach to dynamic boundary problems for level-set curvature flow equations and applications, (with N. Hamamuki), Partial Differ. Equ. Appl., 2 (2021), Article 30.
Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations, (with X. Zhou), Ann. Sc. Norm. Super. Pisa Cl. Sci., 22 (2021), 2039-2076.
Semiconvexity of viscosity solutions to fully nonlinear evolution equations via discrete games, Springer INdAM Series, 47 (2021), Geometric Properties for Parabolic and Elliptic PDE's, 205-231.
The vanishing exponent limit for motion by a power of mean curvature, Interfaces Free Bound., 22 (2020), 51-84.
A deterministic game interpretation for fully nonlinear parabolic equations with dynamic boundary conditions, (with N. Hamamuki), ESAIM Control Optim. Calc. Var., 26 (2020), Paper No. 13, 42 pp.
On a discrete scheme for time fractional fully nonlinear evolution equations, (with Y. Giga and H. Mitake), Asymptot. Anal., 120 (2020), 151-162.
Parabolic Minkowski convolutions and concavity properties of viscosity solutions to fully nonlinear equations, (with K. Ishige and P. Salani), J. Math. Pures Appl., 141 (2020), 342--370.
Large exponent behavior for power-type nonlinear evolution equations and applications, J. Evol. Equ., 20 (2020), 777-810.
On an obstacle problem arising in large exponent asymptotics for one dimensional fully nonlinear diffusions of power type, Adv. Stud. Pure Math., 85 (2020), 281-289.
An obstacle problem arising in large exponent limit of power mean curvature flow equation, (with N. Yamada), Trans. Amer. Math. Soc., 372 (2019), 2103-2141.
Convexity preserving properties for Hamilton-Jacobi equations in geodesic spaces, (with A. Nakayasu), Discrete Contin. Dyn. Syst., 39 (2019), 157-183.
Weakly coupled systems of fully nonlinear parabolic equations in the Heisenberg group, (with X. Zhou), Nonlinear Anal., 174 (2018) 54-78.
Lipschitz continuity and convexity preserving for solutions of semilinear evolution equations in the Heisenberg group, (with J. J. Manfredi and X. Zhou), Calc. Var. Partial Differential Equations, 55 (2016), 55:80.
A nonlinear parabolic equation with discontinuity in the highest order and applications, (with R. M. Chen), J. Differential Equations, 260 (2016), 1200-1227.
A game-theoretic proof of convexity-preserving properties for motion by curvature, (with A. Schikorra and X. Zhou), Indiana Univ. Math. J., 65 (2016), 171-197.
Existence and symmetry of ground states to the Boussinesq abcd systems, (with E. S. Bao and R. M. Chen), Arch. Ration. Mech. Anal., 216 (2015), 569-591.
General existence of solutions to dynamic programming equations, (with A. Schikorra), Commun. Pure Appl. Anal., 14 (2015), a special issue on Emerging Trends in Nonlinear PDE., 167-184.
Large-time asymptotics for Hamilton-Jacobi equations with noncoercive Hamiltonians appearing in crystal growth, (with Y. Giga and H. Mitake), Adv. Stud. Pure Math., 64 (2015), 235-242.
Waiting time effect for motion by positive second derivatives and applications, Nonlinear Differential Equations Appl. NoDEA., 21 (2014), 589-620.
On the characterization of p-harmonic functions on the Heisenberg group by mean value properties, (with F. Ferrari and J. J. Manfredi), Discrete Contin. Dyn. Syst., 34 (2014), 2779-2793.
On the horizontal mean curvature flow for axisymmetric surfaces in the Heisenberg group, (with F. Ferrari and J. J. Manfredi), Commun. Contemp. Math., 16 (2014), 1350027.
Singular Neumann problems and large-time behavior of solutions of noncoercive Hamilton-Jacobi equations, (with Y. Giga and H. Mitake), Trans. Amer. Math. Soc., 366 (2014), 1905-1941.
Large-time asymptotics for one-dimensional Dirichlet problems for Hamilton-Jacobi equations with noncoercive Hamiltonians, (with Y. Giga and H. Mitake), J. Differential Equations, 252 (2012), 1263-1282.
Fattening and comparison principle for level-set equations of mean curvature type, SIAM J. Control Optim., 49 (2011), 2518-2541.
A billiard-based game interpretation of the Neumann problem for the curve shortening equation, (with Y. Giga), Adv. Differential Equations, 14 (2009), 201-240.
A remark on the discrete deterministic game approach for curvature flow equations, (with Y. Giga), GAKUTO Internat. Ser. Math. Sci. Appl., 29 (2008), Nonlinear phenomena with energy dissipation: Mathematical analysis, modeling and simulation, 103-115.
Other publications
Quasiconvexity preserving property for first order nonlocal evolution equations, (with T. Kagaya and H. Mitake), RIMS Kokyuroku, 2277 (2024), 57--69.
Large exponent asymptotics for one dimensional fully nonlinear diffusion of power type, RIMS Kokyuroku, 2146 (2020), 9-20.
On an elementary approach to optimal control with Neumann boundary condition, RIMS Kokyuroku, 1695 (2010), 56-64.
On game interpretations for the curvature flow equation and its boundary problems, RIMS Kokyuroku, 1633 (2009), 138-150.
