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. Pluda, Alessandra, Tonegawa, Yoshihiro, Coarsening phenomena in the network flow, preprint, PDF

2. Stuvard, Salvatore, Tonegawa, Yoshihiro, End-time regularity theorem for Brakke flows, online first, Mathematische Annalen, Open access

3. 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

4. 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

5. Stuvard, Salvatore, Tonegawa, Yoshihiro, Dynamical instability of minimal surfaces at flat singular points, to appear in Journal of Differential Geometry, arXiv:2008.13728

6. 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

7. Kim, Lami, Tonegawa, Yoshihiro, Existence and regularity theorems of one-dimensional Brakke flows, Interfaces and Free Boundaries 22, (2020), 505-550 arXiv:2004.09763

8. 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

9. Tonegwa, Yoshihiro, Brakke's Mean Curvature Flow: An Introduction, Springer Briefs in Mathematics, Springer, 2019 Short introductory book on Brakke flow

10. Kagaya, Takashi, Tonegawa, Yoshihiro, A singular perturbation limit of diffused interface energy with a fixed contact angle condition, Indiana Univ. Math. J. 67No. 4 (2018), 1425–1437arXiv:1609.00191

11. Kagaya, Takashi, Tonegawa, Yoshihiro, A fixed contact angle condition for varifolds, Hiroshima Math. J. 47, (2017) no. 2, 139-153 open access

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. Tonegawa, Yoshihiro, Wickramasekera, Neshan, Stable phase interfaces in the van der Waals-Cahn-Hilliard theory, Journal fur reine und angewandte Mathematik668 (2012), 191-210 arXiv:1007.2060

22. 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

23. 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

24. 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 

25. 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

26. 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 

27. Nagase, Yuko, Tonegawa, Yoshihiro, A singular perturbation problem with integral curvature bound, Hiroshima Math. J. 37 (2007),no. 3, 455-489 Open access

28. Giga, Yoshikazu, Kubo, Motohiko, Tonegawa, Yoshihiro, Magnetic clusters and fold energies, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), no. 1, 23-40 

29. 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

30. 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) 

31. 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)

32. Tonegawa, Yoshihiro, A diffused interface whose chemical potential lies in Sobolev spaces, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 4 (2005) 487-510

33. 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

34. Tonegawa, Yoshihiro, On stable critical points for a singular perturbation problem,Comm. Analysis and Geometry 13, (2005), no. 2, 439--459

35. Tonegawa, Yoshihiro,　Integrality of varifolds in the singular limit of reaction-diffusion equations, Hiroshima Math. J., 33 (2003), no. 3, 323--341 free access

36. 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 

37. Tonegawa Yoshihiro, Domain dependent monotonicity formula for a singular perturbation problem, Indiana Univ. Math. J. 52(2003), 69--84 

38. Tonegawa, Yoshihiro, Phase field model with a variable chemical potential. Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), no. 4, 993--1019

39. 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

40. 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

41. Harris, Adam; Tonegawa, Yoshihiro, Analytic continuation of vector bundles with $L\sp p$-curvature. Internat. J. Math. 11 (2000), no. 1, 29--40

42. Tonegawa, Yoshihiro, Some remarks on the level set flow by anisotropic curvature. Calc. Var. Partial Differential Equations 10 (2000), no. 2, 101--118 

43. 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

44. Tonegawa, Yoshihiro, On the regularity of a chemical reaction interface. Comm. Partial Differential Equations 23 (1998), no. 7-8, 1181--1207 

45. Padilla, Pablo; Tonegawa, Yoshihiro, On the convergence of stable phase transitions. Comm. Pure Appl. Math. 51 (1998), no. 6, 551--579

46. Tonegawa, Yoshihiro, Existence and regularity of constant mean curvature hypersurfaces in hyperbolic space. Math. Z. 221 (1996), no. 4, 591--615 

47. Hardt, Robert; Tonegawa, Yoshihiro, Partial regularity for evolution problems with discontinuity. Manuscripta Math. 90 (1996), no. 1, 85--103

My JSPS grant information

• 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