論文リスト

査読付き論文

[42] Rate of convergence for approximate solutions in obstacle problems for nonlinear operators, (with T. Kosugi), Proceedings in Mathematics & Statistics 451, Mathematical Physics and its Interactions, Springer, (2024), 63-93.

[41] Aleksandrov-Bakelman-Pucci maximum principle for L^p-viscosity solutions of equations with unbounded terms, (with A. A. Święch), Journal de Mathématiques Pures et Appliquées, 168, (2022), 192-212.

[40] Regularity of solutions of obstacle problems -old & new-, Springer Proceedings in Mathematics & Statistics, 346 Nonlinear Partial Differential Equations for Future Applications, (2021), 205-243.

[39] On L^p-viscosity solutions of bilateral obstacle problems with unbounded ingredients, (with S. Tateyama), Mathematische Annalen, 377, (3-4) (2020), 883-910.

[38] Remarks on fully nonlinear uniformly parabolic equations with unbounded ingredients, (with A. Święch, S. Tateyama), Nonlinear Analysis, 185, (2019), 264-289.

[37] On the rate of convergence of solutions in free boundary problems via penalization, (with T. Kosugi, M. Naito), Journal of Maththematical Analysis and Applications, 457(1) (2018), 436-460.

[36] Remarks on mean curvature flow with obstacles, Mathematics for Nonlinear Phenomena: Analysis and Computation, Springer Proc. Math. Statistics, 215 (2017年), 83-103.

[35] Maximum principle for Pucci equations with sublinear growth in Du and its applications, (with T. Kosugi), Nonlinear Analysis, 160 (2017), 1-15.

[34] Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term, (with G. Galise, O. Ley, A. Vitolo), Journal of Mathematical Analysis and Applications, 441(1) (2016), 194-210.

[33] Regularity results and large time behavior for integro-differential equations with coercive Hamiltonians, (with G. Barles, O. Ley, E. Topp), Calculus of Variations, and Partial Differential Equations, 54(1) (2015), 539-572.

[32] Remarks on the comparison principle for quasilinear PDE with no zeroth order terms, (with T. Kosugi), Communications in Pure and Applied Analysis, 14(1) (2015), 133-142.

[31] Representation formulas for solutions of Isaacs integro-PDE, (with A. Święch), Indiana University Mathematical Journal, 62(5) (2013), 1473-1502.

[30] Local maximum principle for L^p-viscosity solutions of fully nonlinear PDEs with unbounded ingredients, (with A. Święch), Communications in Pure and Applied Analysis, 11(5) (2012), 1897-1910.

[29] Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear terms, (with O. Ley), Journal of Mathematical Analysis and Applications, 381(1) (2011), 110-120.

[28] Remarks on the Phragmén-Lindelöf Theorem for L^p-viscosity solutions of fully nonlinear PDEs with unbounded ingredients, (with K. Nakagawa), Electronic Journal of Differential Equations, 2009(146) (2009), 1-14.

[27] Existence of strong solutions of Pucci extremal equations with superlinear growth in Du, (with A. Święch), Journal of the Fixed Point Theory and its Applications, 5(2) (2009), 291-304.

[26] Weak Harnack inequality for fully nonlinear uniformly elliptic PDE with unbounded ingredients, (with A. Święch), Journal of Mathematical Society of Japan, 61(3) (2009), 723-755. 2010 JMSJ Outstanding Paper Prize greeting e-mails

[25] Maximum principle for fully nonlinear equations via the iterated comparison function method, (with A. Święch), Mathematische Annalen, 339(2) (2007), 461-484.

[24] A linear-quadratic control problem with discretionary stopping, (with H. Morimoto, S. Sakaguchi), Discrete and Continuous Dynamical Systems, Series B, 8(2) (2007), 261-277.

[23] Perron's method for L^p-viscosity solutions, Saitama Mathematical Journal, 23 (2005), 9-28.

[22] Optimal consumption and portfolio choice with stopping, (with H. Morimoto), Funkcialaj Ekvacioj, 48(2) (2005), 183-202.

[21] Maximum principle and existence of L^p-viscosity solutions for fully nonlinear uniformly elliptic equations with measurable and quadratic terms, (with A. Święch), Nonlinear Differential Equations Applications, 11(4) (2004), 491-509.

[20] On variational inequalities for leavable boundary-velocity control, (with H. Morimoto), Applied Mathematics and Optimization, 48(1) (2003), 1-20.

[19] Remarks on regularity of viscosity solutions for fully nonlinear uniformly elliptic PDEs with measurable ingredients, (with T. Takahashi) Advances in Differential Equations, 7(4) (2002), 493-512.

[18] On fully nonlinear PDEs derived from variational problems of L^p norms, (with T. Ishibashi), SIAM J. Math. Anal., 33(3) (2001), 545-569.

[17] On ε-optimal controls of state constraint problems (with H. Ishii), Annales de l'Institut Henri Poincare, Analyse Non Lineaire, 14(4), (2000), 473-502.

[16] Uniqueness of lower semicontinuous viscosity solutions for the minimum time problem, (with O. Alvarez and I. Nakayama) SIAM Journal on Control and Optimization, 38(2), (2000), 470-481.

[15] On the pursuit-evasion game with state constraint, (with M. Bardi and P. Soravia) Discrete and Cotinuous Dynamical Systems, 6(2), (2000), 361-380.

[14] Semicontinuous viscosity solutions for Hamilton-Jacobi equations with a degenerate coefficient, Differential and Integral Equations, 10(3) (1997), 455-472.

[13] On the Bellman equations with varying control, Bulletin of the Australian Mathematical Society, 53(1) (1996), 51-62.

[12] A new formulation of state constraint problems for first-order PDEs, (with H. Ishii), SIAM Journal, Control and Optimization, 34(2) (1996), 554-571.

[11] The state constraint problem for differential games, Indiana University Mathematics Journal, 44(2) (1995), 467-487.

[10] Viscosity solutions of monotone systems for Dirichlet problems, (with M. Katsoulakis), Differential and Integral Equations, 7(2) (1994), 367-382.

[9] Viscosity solutions of functional differential equations, (with H. Ishii), Advances in Mathematical Sciences and Applications, 3 (1994), 191-218.

[8] Uniqueness of viscosity solutions for monotone systems of fully nonlinear PDEs under Dirichlet condition, Nonlinear Analysis, Theory, Methods and Applications, 22(4) (1994), 519-532.

[7] Viscosity solutions for monotone systems of second-order elliptic PDEs, (with H. Ishii), Communications in Partial Differential Equations, 16(6-7) (1991), 1095-1128.

[6] Viscosity solutions of a system of nonlinear second-order elliptic PDEs arising in switching games, (with H. Ishii), Funkcialaj Ekvacioj, 34(1) (1991), 143-155.

[5] On the rate of convergence of solutions in singular perturbation problems, Journal of Mathematical Analysis and Applications, 157(1) (1991), 243-253.

[4] Remarks on elliptic singular perturbation problems Remarks on elliptic singular perturbation problems, (with H. Ishii), Applied Mathematics and Optimization, 23(1) (1991), 1-17.

[3] An asymptotic formula for solutions of Hamilton-Jacobi-Bellman equations, Nonlinear Analysis, Theory, Methods and Applications, 11(3) (1987), 429-436.

[2] On the regularity of solutions of a degenerate parabolic Bellman equation, Hiroshima Mathematical Journal, 16(2) (1986), 251-267.

[1] Boundary regularity and uniqueness for an elliptic equation with gradient constraint, (with H. Ishii), Communications in Partial Differential Equations, 8(4) (1983), 317-346.

[38] Nonlinear Partial Differential Equations for Future Applications, Springer Proceedings in Mathematics & Statistics, 346, ed. S. Koike, H. Kozono, T. Ogawa, S. Sakaguchi, 2021.

[37] On the ABP maximum principle for L^p-viscosity solutions of fully nonlinear PDE, Nonlinear Dynamics in Partial Differential Equations, Advanced Studies in Pure Mathematics, 64, (2015), 113-124.

[36] 「粘性解 -比較原理を中心に-」(2015), 共立出版.

[35] On the ABP maximum principle for L^p-viscosity solutions of fully nonlinear PDE, Nonlinear Dynamics in Partial Differential Equations, Advanced Studies in Pure Mathematics, 64, (2015), 113-124.

[34] On the ABP maximum principle and applications, 数理解析研究所講究録1845「幾何学的偏微分方程式における保存則と正則性の研究」 (2013), 107-120.

[33] Weak Harnack inequality for fully nonlinear PDEs with superlinear growth terms in Du, Surikaisekikenkyusho Kokyuroku 1695 (2010), 139-147.

[32] Viscosity solution method in nonlinear partial differential equations, Mathematics of Complexity and Dynamical Systems, Springer, New-York, (1-3), (2012), 1115-1125.

[31] 粘性解, 数学辞典, 朝倉書店, 2page, submitted.

[30]テキスト理系の数学1, リメディアル数学, 泉屋周一, 上江洌達也, 小池茂昭, 重本和泰, 徳永浩雄, 数学書房, 2011.　 訂正

[29] 粘性解が古典解になる時 -Caffarelliの研究の紹介-, 数学 第62巻 第9号, 2010年, 315-328.

[28] テキスト理系の数学2, 微分積分, 数学書房, 2010.

[27] Recent developments on maximum principle for L^p viscosty solutions of fully nonlinear elliptic/parabolic PDEs, Recent Progress on Reaction-Diffusion Systems and Viscosity Solutions, Y. Du, H. Ishii, W.-Y. Lin, World Scientific, 131-153, 2009.

[26] Proceedings of the International Conference on the 25th Anniversary of Viscosity Solutions, edited by Y. Giga, K. Ishii, S. Koike, T. Ozawa, N. Yamada, Gakkotosho, 2008.

[25] Perron-Ishii method for viscosity solutions, Surikaisekikenkyusho Kokyuroku, 1553 (2007), 44-58 (in Japanese)

[24] 数学辞典(一部), 岩波書店, 2007.

[23] 数理ファイナンスに現れる偏微分方程式, これからの非線型偏微分方程式, 日本評論社, 2007, 151-168.

[22] Maximum principle via the iterated comparison function method, Surikaisekikenkyusho Kokyuroku, 1545 (2007), 1-12.

[21] Perron's method -revisited- (ペロンの方法-revisited-in Japanese), the Proceedings of PDEs and Phenomena in Miyazaki 2004, (2005), 90-97.

[20] Perron's method -revisited-, Surikaisekikenkyusho Kokyuroku, 1428 (2005), 1-8.

[19] Characterization of value functions via viscosity solutions ( 粘性解による値関数の特徴づけ in Japansese), (with Y. Giga), System/Seigyo/Joho (システム/制御/ 情報) 49(1) (2005), 2-7.

[18] A Beginner's Guide to the Theory of Viscosity Solutions, MSJ Memoir, 13, Math. Soc. Japan, Tokyo, 2004. 第二版(無料)

[17] On fully nonlinear PDEs with quadratic nonlinearity, Surikaisekikenkyusho Kokyuroku 1287 (2002), 1-11.

[16] Interior Hölder estimates for fully nonlinear uniformly elliptic second-order PDEs with measurable and quadratic ingredients, Surikaisekikenkyusho Kokyuroku 1242 (2002), 16-29.

[15] On a class of fully nonlinear PDEs derived from variational problems of L^p norms, (with T. Ishibashi), Surikaisekikenkyusho Kokyuroku, 1197 (2001), 84-94.

[14] Tiny results on L^p-viscosity solutions of fully nonlinear uniformly elliptic equations, Proceedings of the Tenth Tokyo Conference on Nonlinear PDE 2000, 10-19.

[13] ε-optimal controls for state constraint problems, Surikaisekikenkyusho Kokyuroku 1135 (2000), 110-119.

[12] A new method of construction of ε-optimal feedback controls from Hamilton-Jacobi equations, Proceedings of the Ninth Tokyo Conference on Nonlinear PDE 1999, 14-22.

[11] Introduction to the viscosity solution theory of first order PDEs, Surikaisekikenkyusho Kokyuroku, 1111 (1999), 107-116.

[10] Lower semicontinuous viscosity solutions for the minimum time problem, Proceedings of the Sixth Tokyo Conference on Nonlinear PDE 1997, (1997), 75-83.

[9] A comparison result for the state constraint problem of differential games, Proceeding of Korea-Japan Partial Differential Equations Conference, 39, 1997.

[8] Semicontinuous solutions for Hamilton-Jacobi equations with degeneracy, Surikaisekikenkyusho Kokyuroku 973 (1996), 120-130.

[7] Viscosity solution theory for nonlinear partial differential equations (Works of Hitoshi Ishii), (with N. Yamada), Sugaku 47 (in Japanese), (1995), 176-184.

[6] On the state constraint boundary condition for Isaacs equations, Surikaisekikenkyusho Kokyuroku 911 (1995), 20-28.

[5] A viscosity solution approach to functional differential equations, Proceedings of the Second GARC SYMPOSIUM on Pure and Applied Mathematics, 17 (1993), 213-219.

[4] Viscosity solutions for monotone systems under Dirichlet condition, Surikaisekikenkyusho Kokyuroku 785, (1992), 62-75.

[3] On the rate of convergence in singular perturbations of obstacle problems, Surikaisekikenkyusho Kokyuroku 679, (1989), 163-173.

[2] Applications to singular perturbation problems via viscosity solution method, (with H. Ishii), Surikaisekikenkyusho Kokyuroku 647 (in Japanese), (1988), 1-12.

[1] On an asymptotic formula of solutions of Hamilton-Jacobi-Bellman equations, Surikaisekikenkyusho Kokyuroku 604 (in Japanese), (1987), 20-31.