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 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

• 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. Tonegawa, Yoshihiro, Tsukamoto, Yuki, A diffused interface with the advection term in a Sobolev space, submitted arXiv:1904.00525
2. Tonegwa, Yoshihiro, Brakke's Mean Curvature Flow: An Introduction, Springer Briefs in Mathematics, Springer, 2019
3. 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
4. Kagaya, Takashi, Tonegawa, Yoshihiro, A fixed contact angle condition for varifolds, Hiroshima Math. J. 47, (2017) no. 2, 139-153 free access
5. Kim, Lami, Tonegawa, Yoshihiro, On the mean curvature flow of grain boundaries, Annales de l'Institut Fourier (Grenoble) 67, (2017) no. 1, 43-142 free download
6. 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
7. 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
8. 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
9. 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
10. 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
11. 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
12. 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
13. 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
14. 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
15. 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
16. 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
17. 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
18. 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
19. 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
20. Nagase, Yuko, Tonegawa, Yoshihiro, A singular perturbation problem with integral curvature bound, Hiroshima Math. J. 37 (2007),no. 3, 455-489 free access
21. Giga, Yoshikazu, Kubo, Motohiko, Tonegawa, Yoshihiro, Magnetic clusters and fold energies, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), no. 1, 23-40
22. 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
23. 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)
24. 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)
25. Tonegawa, Yoshihiro, A diffused interface whose chemical potential lies in Sobolev spaces, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 4 (2005) 487-510
26. 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
27. Tonegawa, Yoshihiro, On stable critical points for a singular perturbation problem,Comm. Analysis and Geometry 13, (2005), no. 2, 439--459
28. Tonegawa, Yoshihiro,　Integrality of varifolds in the singular limit of reaction-diffusion equations, Hiroshima Math. J., 33 (2003), no. 3, 323--341 free access
29. 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
30. Tonegawa Yoshihiro, Domain dependent monotonicity formula for a singular perturbation problem, Indiana Univ. Math. J. 52(2003), 69--84
31. Tonegawa, Yoshihiro, Phase field model with a variable chemical potential. Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), no. 4, 993--1019
32. 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
33. 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
34. Harris, Adam; Tonegawa, Yoshihiro, Analytic continuation of vector bundles with $L\sp p$-curvature. Internat. J. Math. 11 (2000), no. 1, 29--40
35. Tonegawa, Yoshihiro, Some remarks on the level set flow by anisotropic curvature. Calc. Var. Partial Differential Equations 10 (2000), no. 2, 101--118
36. 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
37. Tonegawa, Yoshihiro, On the regularity of a chemical reaction interface. Comm. Partial Differential Equations 23 (1998), no. 7-8, 1181--1207
38. Padilla, Pablo; Tonegawa, Yoshihiro, On the convergence of stable phase transitions. Comm. Pure Appl. Math. 51 (1998), no. 6, 551--579
39. Tonegawa, Yoshihiro, Existence and regularity of constant mean curvature hypersurfaces in hyperbolic space. Math. Z. 221 (1996), no. 4, 591--615
40. 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) 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