Hardy Chan

About me

My favorite function is the hyperbolic tangent, which is a typical solution of the Allen–Cahn equation.

- Office address:

HG F 28.6, Department of Mathematics

ETH Zürich

Rämistrasse 101, 8092 Zürich

Switzerland - Phone:

+41 44 632 82 90

I am interested in nonlinear partial differential equations arising from geometry and natural sciences. A large part of my research stems from two classical equations - the Allen–Cahn equation in phase transition, which is deeply connected to minimal surfaces and pattern formation, as well as the Lane–Emden equation in astrophysics, which includes in particular the Yamabe problem, a central question in conformal geometry. I study also the corresponding long range interaction models that have been recently prevalent.

Previously I was a Ph.D. student at the University of British Columbia, where I learned how to obtain solutions. My advisors were Prof. Nassif Ghoussoub and Prof. Juncheng Wei.

Even before, I completed my M.Phil. at the Chinese University of Hong Kong, under the supervision of Prof. Kai Seng Chou.

Research

# | Coauthors | Title | Journal | Article |
---|---|---|---|---|

María del Mar González, Yanghong Huang, Edoardo Mainini, Bruno Volzone | Uniqueness of entire ground states for the fractional plasma problem | Calc. Var. PDE 59 (2020), no. 6, Art. 195, 42 pp. | ||

Weiwei Ao, María del Mar González, Juncheng Wei | Bound state solutions for the supercritical fractional Schrödinger equation | Nonlinear Anal. 193 (2020), 111448, 21 pp. | ||

Azahara DelaTorre | An analytic construction of singular solutions related to a critical Yamabe problem | Comm. PDE (2020), 1784209, 26 pp. | ||

Weiwei Ao, Azahara DelaTorre, Marco A. Fontelos, María del Mar González, Juncheng Wei | On higher-dimensional singularities for the fractional Yamabe problem: A nonlocal Mazzeo–Pacard program | Duke Math. J. 168 (2019), no. 17, 3297–3411 | ||

Masomeh Jamshid Nejad, Juncheng Wei | Lamellar phase solutions for diblock copolymers with nonlocal diffusions | Phys. D 388 (2019), 22–32 | ||

Juncheng Wei | On De Giorgi’s conjecture: recent progress and open problems | Sci. China Math. 61 (2018), no. 11, 1925–1946 | ||

Nassif Ghoussoub, Saikat Mazumdar, Shaya Shakerian, Luis Fernando de Oliveira Faria | Mass and extremals associated with the Hardy–Schrödinger operator on hyperbolic space | Adv. Nonlinear Stud. 18 (2018), no. 4, 671–689 | ||

/ | The multiplier problem of the calculus of variations for scalar ordinary differential equations | Calc. Var. PDE 57 (2018), no. 2, Art. 40, 32 pp. | ||

Weiwei Ao, María del Mar González, Juncheng Wei | Existence of positive weak solutions for fractional Lane–Emden equations with prescribed singular sets | Calc. Var. PDE 57 (2018), no. 6, Art. 149, 25 pp. | ||

Weiwei Ao, Juncheng Wei | Boundary concentrations on segments for the Lin–Ni–Takagi problem | Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 18 (2018), no. 2, 653–696 | ||

Juncheng Wei | Traveling wave solutions for bistable fractional Allen–Cahn equations with a pyramidal front | J. Differential Equations 262 (2017), no. 9, 4567–4609 |

# | Coauthors | Title | arXiv | Journal |
---|---|---|---|---|

David Gómez-Castro, Juan Luis Vázquez | Blow-up phenomena in nonlocal eigenvalue problems: when theories of $L^1$ and $L^2$ meet | 2004.04579 | J. Funct. Anal. | |

Weiwei Ao, Azahara DelaTorre, Marco A. Fontelos, María del Mar González, Juncheng Wei | ODE-methods in non-local equations | 1910.14512 | J. Math. Study | |

Yannick Sire, Liming Sun | Convergence of the fractional Yamabe flow for a class of initial data | 1809.05753 | Ann. Sc. Norm. Super. Pisa Cl. Sci. |

# | Coauthors | Title | arXiv |
---|---|---|---|

David Gómez-Castro, Juan Luis Vázquez | Singular solutions for fractional parabolic boundary value problems | 2007.13391 | |

Yong Liu, Juncheng Wei | Existence and instability of deformed catenoidal solutions for fractional Allen–Cahn equation | 1711.03215 | |

Luis Fernando de Oliveira Faria, Shaya Shakerian | A variational problem associated to a hyperbolic Caffarelli–Kohn–Nirenberg inequality | 1711.05927 |

# | Coauthors | Description |
---|---|---|

Alessio Figalli, Joaquim Serra | Local/nonlocal/free boundary Allen-Cahn equations | |

Juan Dávila, Manuel del Pino, Yong Liu, Juncheng Wei | Counter-examples for fractional De Giorgi conjecture for 1/2 < s < 1 | |

Xavier Cabré, Juncheng Wei | Nonlocal minimizing cones | |

María del Mar González, Juncheng Wei | Yamabe problem with conical singularity / blow-up in fractional heat flow | |

Azahara DelaTorre | Singular solutions for a critical fractional Yamabe problem | |

/ | Boundary regularity of a non-variational nonlocal operator | |

David Gómez-Castro, Juan Luis Vázquez | Space-time fractional problems with boundary singularity | |

Yannick Sire | Moduli space of Escobar metrics |