Department of Mathematics
Tokyo Institute of Technology

2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, JAPAN
email address: my last name and at mark and math.titech.ac.jp

Research

Research interests

  • Partial differential equations of elliptic and parabolic types
  • Geometric measure theory and its applications
  • Calculus of variations
  • Allen-Cahn equation and Cahn-Hillard equation
  • Minimal surface and mean curvature flow

Textbooks I ask my graduate students to read

  • Partial differential equations, L.C. Evans
  • Minimal surfaces and functions of bounded variation, E. Giusti
  • Cartesian currents in the calculus of variations I,II, Giaquinta et al

Lectures on Video

  • Fourier Institute (Grenoble, France), Summer school on geometric measure theory and calculus of variations (6/15-18/2015, 8 hour mini course) Link
  • International Centre for Theoretical Physics (Trieste, Italy), International school on Extrinsic curvature flows (6/4-15/2018, 6 hour mini course) Link
  • Hausdorff Research Instituite (Bonn, Germany), Winter school on Interfaces in Geometry and Fluids(1/7-11/2019, 6 hour mini course) Link

    Edited books

    1. Variational Methods for Evolving Objects, Edited by L. Ambrosio, Y. Giga, P. Rybka, Y. Tonegawa, Advanced Studies in Pure Mathematics, Vol. 67, (2015) 298pp

    Publications

    1. Stuvard, Salvatore, Tonegawa, Yoshihiro, End-time regularity theorem for Brakke flows, to appear in Mathematische Annalen, arXiv:2212.07727
    2. Stuvard, Salvatore, Tonegawa, Yoshihiro, On the existence of canonical multi-phase Brakke flows, Advances in Calculus of Variations 17, no. 1, (2024) 33-78 Open access
    3. Mori, Ryunosuke, Tomimatsu, Eita, Tonegawa, Yoshihiro, Brakke's formulation of velocity and the second order regularity property, Indiana University Math. J. 72, no. 5, (2023) 1909-1930 arXiv:2109.06380
    4. Stuvard, Salvatore, Tonegawa, Yoshihiro, Dynamical instability of minimal surfaces at flat singular points, submitted arXiv:2008.13728
    5. Stuvard, Salvatore, Tonegawa, Yoshihiro, An existence theorem for Brakke flow with fixed boundary conditions, Calc. Var. Partial Differential Equations 60, no. 1, 43 (2021) 53pp Open access
    6. Kim, Lami, Tonegawa, Yoshihiro, Existence and regularity theorems of one-dimensional Brakke flows, Interfaces and Free Boundaries 22, (2020), 505-550 arXiv:2004.09763
    7. Tonegawa, Yoshihiro, Tsukamoto, Yuki, A diffused interface with the advection term in a Sobolev space, Calc. Var. Partial Differential Equations 59, no. 6, 184 (2020) 23pp Open access
    8. Tonegwa, Yoshihiro, Brakke's Mean Curvature Flow: An Introduction, Springer Briefs in Mathematics, Springer, 2019 Short introductory book on Brakke flow
    9. Kagaya, Takashi, Tonegawa, Yoshihiro, A singular perturbation limit of diffused interface energy with a fixed contact angle condition, Indiana Univ. Math. J. 67 No. 4 (2018), 1425–1437arXiv:1609.00191
    10. Kagaya, Takashi, Tonegawa, Yoshihiro, A fixed contact angle condition for varifolds, Hiroshima Math. J. 47, (2017) no. 2, 139-153 open access
    11. Kim, Lami, Tonegawa, Yoshihiro, On the mean curvature flow of grain boundaries, Annales de l'Institut Fourier (Grenoble) 67, (2017) no. 1, 43-142 open access
    12. Riku Takahashi, Yumihiko Ikura, Daniel Rudolf King, Takayuki Nonoyama, Tasuku Nakajima, Takayuki Kurokawa, Hirotoshi Kuroda, Yoshihiro Tonegawa and Jian Ping Gong, Coupled instabilities of surface crease and bulk bending during fast free swelling of hydrogel, Soft Matter (2016) 12, 5081-5088 open access
    13. Tonegawa, Yoshihiro, Wickramasekera, Neshan, The blow up method for Brakke flows: networks near triple junctions, Archive for Rational Mechanics and Analysis 221, (2016) no. 3, 1161-1222 arXiv:1504.01212
    14. Takasao, Keisuke, Tonegawa, Yoshihiro, Existence and regularity of mean curvature flow with transport term in higher dimensions, Mathematische Annalen 364, (2016) no. 3-4, 857-935 arXiv:1307.6629
    15. Mizuno, Masashi, Tonegawa, Yoshihiro, Convergence of the Allen-Cahn equation with Neumann boundary conditions, SIAM Journal on Mathematical Analysis 47, (2015) no. 3, 1906-1932 arXiv:1403.5624
    16. Tonegawa, Yoshihiro, A second derivative Hoelder estimate for weak mean curvature flow, Advances in Calculus of Variations 7, (2014) no. 1, 91-138 arXiv:1204.4571
    17. Kasai, Kota, Tonegawa, Yoshihiro, A general regularity theory for weak mean curvature flow, Calc. Var. Partial Differential Equations 50, (2014) no. 1, 1-68 arXiv:1111.0824
    18. Tonegawa, Yoshihiro, Introduction to varifold and its curvature flow, Emerging topics on differential equations and their applications, 213–226, Nankai Ser. Pure Appl. Math. Theoret. Phys., 10, World Sci. Publ., Hackensack, NJ, 2013
    19. Liu, Chun, Sato, Norifumi, Tonegawa, Yoshihiro, Two-phase flow problem coupled with mean curvature flow, Interfaces and Free Boundaries 14, (2012) no. 2, 185-203 arXiv:1102.4054
    20. Tonegawa, Yoshihiro, Wickramasekera, Neshan, Stable phase interfaces in the van der Waals-Cahn-Hilliard theory, Journal fur reine und angewandte Mathematik 668 (2012), 191-210 arXiv:1007.2060
    21. Liu, Chun, Sato, Norifumi, Tonegawa, Yoshihiro, On the existence of mean curvature flow with transport term, Interfaces and Free Boundaries 12, (2010), no. 2, 251-277
    22. Tonegawa, Yoshihiro, Applications of geometric measure theory to two-phase separation problems [translation of Sugaku 57 (2005), no. 2, 178-196] Sugaku Expositions 21 (2008), no. 1, 97-115
    23. Hong, Ming-Chun, Tonegawa, Yoshihiro, Yassin, Alzubaidi, Partial regularity of weak solutions to Maxwell's equation in quasi-static electromagnetic field, Methods and Applications of Analysis 15, (2008) no. 2, 205-222
    24. Roeger, Matthias, Tonegawa, Yoshihiro, Convergence of phase-field approximations to the Gibbs-Thomson law, Calc. Var. Partial Differential Equations 32, (2008) no. 1, 111-136 Open access
    25. Westdickenberg (Reznikoff), Maria, Tonegawa, Yoshihiro, Higher multiplicities in the one-dimensional Allen-Cahn action functional, Indiana University Math. Journal 56, (2007) no 6, 2935-2989
    26. Nagase, Yuko, Tonegawa, Yoshihiro, A singular perturbation problem with integral curvature bound, Hiroshima Math. J. 37 (2007),no. 3, 455-489open access
    27. Giga, Yoshikazu, Kubo, Motohiko, Tonegawa, Yoshihiro, Magnetic clusters and fold energies, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), no. 1, 23-40
    28. Kohn, Robert, Reznikoff, Maria, Tonegawa, Yoshihiro, Sharp-interface limit of the action functional for Allen Cahn in one space dimension, Calc. Var. Partial Differential Equations 25, (2006) no. 4 503-534
    29. Nagase, Yuko, Tonegawa, Yoshihiro, Interior gradient estimate for 1-D anisotropic curvature flow, Boletim da Sociedade Paranaense de Matematica 23 no. 1-2, 93-98 (2005)
    30. Tonegawa, Yoshihiro, Umeda, Noriaki, Hayakawa, Tohru, Ishibashi, Teruo, Evaluation of data in terms of two-dimensional random walk model: Interaction between NADH-cytochrome b5 reductase and cytochrome b5, Biomedical Research 26 (5) 207--212 (2005)
    31. Tonegawa, Yoshihiro, A diffused interface whose chemical potential lies in Sobolev spaces, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 4 (2005) 487-510
    32. Chen, Yunmei, Rao, M., Tonegawa, Y., Wunderli, T., Partial regularity for a selective smoothing functional for image restoration in BV space, SIAM Journal on Mathematical Analysis 37, (2005), no. 4, 1098 - 1116
    33. Tonegawa, Yoshihiro, On stable critical points for a singular perturbation problem,Comm. Analysis and Geometry 13, (2005), no. 2, 439--459
    34. Tonegawa, Yoshihiro, Integrality of varifolds in the singular limit of reaction-diffusion equations, Hiroshima Math. J., 33 (2003), no. 3, 323--341 free access
    35. Harris, Adam, Tonegawa, Yoshihiro, A $\bar{\partial}\partial$-Poincare lemma for forms near an isolated complex singularity, Proc. Amer. Math. Soc 131 (2003), 3329--3334
    36. Tonegawa Yoshihiro, Domain dependent monotonicity formula for a singular perturbation problem, Indiana Univ. Math. J. 52(2003), 69--84
    37. Tonegawa, Yoshihiro, Phase field model with a variable chemical potential. Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), no. 4, 993--1019
    38. Harris, Adam; Tonegawa, Yoshihiro, $L\sp p$-curvature and the Cauchy-Riemann equation near an isolated singular point. Nagoya Math. J.164 (2001), 35--51
    39. Flores, Gilberto; Padilla, Pablo; Tonegawa, Yoshihiro, Higher energy solutions in the theory of phase transitions: a variational approach. Part 3 (Atlanta, GA/Lisbon, 1998). J. Differential Equations 169 (2001), no. 1, 190--207
    40. Harris, Adam; Tonegawa, Yoshihiro, Analytic continuation of vector bundles with $L\sp p$-curvature. Internat. J. Math. 11 (2000), no. 1, 29--40
    41. Tonegawa, Yoshihiro, Some remarks on the level set flow by anisotropic curvature. Calc. Var. Partial Differential Equations 10 (2000), no. 2, 101--118
    42. Hutchinson, John E.; Tonegawa, Yoshihiro, Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory. Calc. Var. Partial Differential Equations 10 (2000), no. 1, 49--84
    43. Tonegawa, Yoshihiro, On the regularity of a chemical reaction interface. Comm. Partial Differential Equations 23 (1998), no. 7-8, 1181--1207
    44. Padilla, Pablo; Tonegawa, Yoshihiro, On the convergence of stable phase transitions. Comm. Pure Appl. Math. 51 (1998), no. 6, 551--579
    45. Tonegawa, Yoshihiro, Existence and regularity of constant mean curvature hypersurfaces in hyperbolic space. Math. Z. 221 (1996), no. 4, 591--615
    46. Hardt, Robert; Tonegawa, Yoshihiro, Partial regularity for evolution problems with discontinuity. Manuscripta Math. 90 (1996), no. 1, 85--103

    JSPS Grant

    • Grant-in-aid for scientific research (A) 2023-2027 #23H00085
    • Grant-in-aid for scientific research (A) 2018-2022 #18H03670
    • Grant-in-aid for scientific research (A) 2013-2017 #25247008
    • Grant-in-aid for challenging exploratory research 2011-2013 #23654057
    • Grant-in-aid for scientific research (B) 2009-2012 #21340033
    • Grant-in-aid for scientific research (B) 2005-2008 #17340041
    • Grant-in-aid for young scientist (A) 2002-2004 #14702001
    • Grant-in-aid for research promotion (A) 2000-2001#12740112