Publications

Refereed papers

  • Horizontally quasiconvex envelope in the Heisenberg group, (with A. Kijowski and X. Zhou), preprint. 
  • Quasiconvexity presering property for fully nonlinear nonlocal parabolic equations, (with T. Kagaya and H. Mitake), preprint.
  • Principal eigenvalue problem for infinity Laplacian in metric spaces, (with A. Mitsuishi), submitted for publication.
  • Differential games and Hamilton-Jacobi-Isaacs equations in metric spaces, (with X. Zhou), to appear in Minimax Theory Appl. 
  • 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

  • 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.