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
- 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
- Stuvard, Salvatore, Tonegawa, Yoshihiro, End-time regularity theorem for
Brakke flows, to appear in Mathematische Annalen, arXiv:2212.07727
- 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
- 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
- Stuvard, Salvatore, Tonegawa, Yoshihiro, Dynamical instability of minimal surfaces at flat singular points, submitted arXiv:2008.13728
- 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
- Kim, Lami, Tonegawa, Yoshihiro, Existence and regularity theorems of one-dimensional
Brakke flows, Interfaces and Free Boundaries 22, (2020), 505-550 arXiv:2004.09763
- 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
- Tonegwa, Yoshihiro, Brakke's Mean Curvature Flow: An Introduction, Springer Briefs in Mathematics, Springer, 2019 Short introductory book on Brakke flow
- 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
- Kagaya, Takashi, Tonegawa, Yoshihiro, A fixed contact angle condition for
varifolds, Hiroshima Math. J. 47, (2017) no. 2, 139-153 open access
- 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
- 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
- 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
- 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
- Mizuno, Masashi, Tonegawa, Yoshihiro, Convergence of the Allen-Cahn equation
with Neumann boundary conditions, SIAM Journal on Mathematical Analysis 47, (2015) no. 3, arXiv:1403.5624
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Nagase, Yuko, Tonegawa, Yoshihiro, A singular perturbation problem with
integral curvature bound, Hiroshima Math. J. 37 (2007),no. 3, 455-489open access
- Giga, Yoshikazu, Kubo, Motohiko, Tonegawa, Yoshihiro, Magnetic clusters
and fold energies, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), no. 1, 23-40
- 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
- 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)
- 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)
- Tonegawa, Yoshihiro, A diffused interface whose chemical potential lies in Sobolev spaces, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 4 (2005) 487-510
- 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
- Tonegawa, Yoshihiro, On stable critical points for a singular perturbation
problem,Comm. Analysis and Geometry 13, (2005), no. 2, 439--459
- Tonegawa, Yoshihiro, Integrality of varifolds in the singular limit of
reaction-diffusion equations, Hiroshima Math. J., 33 (2003), no. 3, 323--341 free access
- 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
- Tonegawa Yoshihiro, Domain dependent monotonicity formula for a singular
perturbation problem, Indiana Univ. Math. J. 52(2003), 69--84
- Tonegawa, Yoshihiro, Phase field model with a variable chemical potential.
Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), no. 4, 993--1019
- 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
- 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
- Harris, Adam; Tonegawa, Yoshihiro, Analytic continuation of vector bundles
with $L\sp p$-curvature. Internat.
J. Math. 11 (2000), no. 1, 29--40
- Tonegawa, Yoshihiro, Some remarks on the level set flow by anisotropic
curvature. Calc.
Var. Partial Differential Equations 10 (2000), no. 2, 101--118
- 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
- Tonegawa, Yoshihiro, On the regularity of a chemical reaction interface.
Comm.
Partial Differential Equations 23 (1998), no. 7-8, 1181--1207
- Padilla, Pablo; Tonegawa, Yoshihiro, On the convergence of stable phase
transitions. Comm.
Pure Appl. Math. 51 (1998), no. 6, 551--579
- Tonegawa, Yoshihiro, Existence and regularity of constant mean curvature hypersurfaces in hyperbolic space. Math.
Z. 221 (1996), no. 4, 591--615
- Hardt, Robert; Tonegawa, Yoshihiro, Partial regularity for evolution problems
with discontinuity. Manuscripta
Math. 90 (1996), no. 1, 85--103
- 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