then he saw [wisdom] and declared it, yes, he set it up and searched it out...
Job 28, The Hebrew Bible
Dr. Hon To Hardy Chan
Lehrbeauftragter (Fachbereich Mathematik)
Büro
Departement Mathematik und Informatik
Spiegelgasse 1
4051 Basel
Schweiz
Wissenschaftlicher Mitarbeiter (FG Lenzmann)
Büro
Spiegelgasse 1
4051 Basel
Schweiz
Elliptic PDEs: Theory and Applications (FS 2025, 74783-01)
Lecture dates: Thursdays, from 20.02.2025 to 29.05.2025, except 13.03.2025 (Fasnachstferien), 20.03.2025 (conference), 17.04.2025 (Ostern), 01.05.2025 (Tag der Arbeit), 29.05.2025 (Auffahrt).
Lecture time: 10.15-12.00
Lecture room: Kollegienhaus, Hörsaal 119
Practical course dates: Mondays, from 24.02.2025 to 19.05.2025, except 10.03.2025 (Fasnachstferien), 17.03.2025 (conference), 21.04.2025 (Ostern).
Practical course time: 14.15-16.00
Practical course room: Spiegelgasse 5, Seminarraum 05.002
Exam date: Monday, 26.05.2025
Exam time: 14.15-16.00
Exam room: Spiegelgasse 5, Seminarraum 05.002
References:
S. Dipierro and E. Valdinoci, Elliptic partial differential equations from an elementary viewpoint---a fresh glance at the classical theory, World Sci. Publ., Hackensack, NJ, [2024]; MR4784613
L. C. Evans, Partial differential equations, Graduate Studies in Mathematics, 19, Amer. Math. Soc., Providence, RI, 1998; MR1625845
X. Fern\'andez-Real and X. Ros-Oton, Regularity theory for elliptic PDE, Zurich Lectures in Advanced Mathematics, 28, EMS Press, Berlin, [2022]; MR4560756
D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, reprint of the 1998 edition, Classics in Mathematics, Springer, Berlin, 2001; MR1814364
Curriculum Vitae
2022-present
SNF Ambizione Fellow (PI)
2021-2022
Severo Ochoa Postdoctoral Fellow (ICMAT, Madrid)
2018-2021
ERC Postdoctoral Fellow (ETH Zurich)
Ph.D. (2018)
Dissertation "New solutions to local and non-local elliptic equations." under Juncheng Wei and Nassif Ghoussoub, University of British Columbia
M.Phil. (2013)
Thesis "Convergence of bounded solutions for nonlinear parabolic equations" under Kai-Seng Chou, Chinese University of Hong Kong
Research Interests
Nonlinear partial differential equations, semilinear elliptic equations, nonlocal equations, phase transitions, Yamabe problem, nonlocal minimal surfaces, construction of solutions, singular solutions, free boundary problems
Major Scientific Achievements
Flatness of stable free boundary, classificaiton of stable nonlocal minimal surfaces, theory of nonlocal ODEs, fractional elliptic gluing scheme, new boundary singular phenomena
Selected publication(s)
W. Ao, H. Chan, A. DelaTorre, M.A. Fontelos, M.d.M. Gonzalez, J. Wei. On higher-dimensional singularities for the fractional Yamabe problem: A nonlocal Mazzeo–Pacard program, Duke Math. J. 168 (2019), no. 17, 3297–3411.
Preprints
H. Chan, X. Fernandez-Real, A. Figalli, J. Serra, Stable free boundaries in dimension 3:Allen–Cahn and Alt–Caffarelli, forthcoming.
H. Chan, S. Dipierro, J. Serra, E. Valdinoci. Nonlocal approximation of minimal surfaces: optimal estimates from stability, arXiv:2308.06328.
H. Chan, Y. Liu, J. Wei. Existence and instability of deformed catenoidal solutions for fractional Allen–Cahn equation, arXiv:1711.03215.