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幾何と解析の両方に興味があります.といってもかなり解析よりで、幾何学的な問題を解析的な手法、特に測度論や微分方程式を使って切り込むといった感じです.キーワード的には以下のようです. 担当科目 




  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 日本語リンク
  1. Kagaya, Takashi, Tonegawa, Yoshihiro, A singular perturbation limit of diffused interface energy with a fixed contact angle condition, appeared online, Indiana University Math. J. arXiv:1609.00191
  2. Kagaya, Takashi, Tonegawa, Yoshihiro, A fixed contact angle condition for varifolds, Hiroshima Math. J. 47, (2017) no. 2, 139-153 arXiv:1606.00164
  3. Kim, Lami, Tonegawa, Yoshihiro, On the mean curvature flow of grain boundaries, Annales de l'Institut Fourier (Grenoble) 67, (2017) no. 1, 43-142 PDF
  4. 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 DOI: 10.1039/C6SM00578K
  5. 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 Featured article in Advances in Engineering
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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 article
  17. 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
  18. Nagase, Yuko, Tonegawa, Yoshihiro, A singular perturbation problem with integral curvature bound, Hiroshima Math. J. 37 (2007),no. 3, 455-489
  19. Giga, Yoshikazu, Kubo, Motohiko, Tonegawa, Yoshihiro, Magnetic clusters and fold energies, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), no. 1, 23-40
  20. 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
  21. 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)
  22. 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)
  23. Tonegawa, Yoshihiro, A diffused interface whose chemical potential lies in Sobolev spaces, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 4 (2005) 487-510
  24. 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
  25. Tonegawa, Yoshihiro, On stable critical points for a singular perturbation problem,Comm. Analysis and Geometry 13, (2005), no. 2, 439--459
  26. Tonegawa, Yoshihiro, Integrality of varifolds in the singular limit of reaction-diffusion equations, Hiroshima Math. J. 33, (2003), no. 3, 323--341
  27. 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
  28. Tonegawa Yoshihiro, Domain dependent monotonicity formula for a singular perturbation problem,Indiana Univ. Math. J. 52 (2003), 69--84
  29. Tonegawa, Yoshihiro, Phase field model with a variable chemical potential. Proc. Roy. Soc. Edinburgh Sect. A 132(2002), no. 4, 993--1019
  30. 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
  31. 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
  32. Harris, Adam; Tonegawa, Yoshihiro, Analytic continuation of vector bundles with $L\sp p$-curvature. Internat. J. Math. 11(2000), no. 1, 29--40
  33. Tonegawa, Yoshihiro, Some remarks on the level set flow by anisotropic curvature. Calc. Var. Partial Differential Equations 10 (2000), no. 2, 101--118
  34. 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
  35. Tonegawa, Yoshihiro, On the regularity of a chemical reaction interface. Comm. Partial Differential Equations 23(1998), no. 7-8, 1181--1207
  36. Padilla, Pablo; Tonegawa, Yoshihiro, On the convergence of stable phase transitions. Comm. Pure Appl. Math. 51(1998), no. 6, 551--579
  37. Tonegawa, Yoshihiro, Existence and regularity of constant mean curvature hypersurfaces in hyperbolic space. Math. Z. 221(1996), no. 4, 591--615
  38. Hardt, Robert; Tonegawa, Yoshihiro, Partial regularity for evolution problems with discontinuity. Manuscripta Math. 90 (1996), no. 1, 85--103

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