Hardy Chan


About me

I am an ERC Postdoctoral Fellow of Prof. Dr. Alessio Figalli at ETH Zürich. We are studying the rigidity of stable solutions in phase transition models.

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



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



Publications



# 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. .pdf
Weiwei Ao, María del Mar González, Juncheng Wei Bound state solutions for the supercritical fractional Schrödinger equation Nonlinear Anal. 193 (2020), 111448, 21 pp. .pdf
Azahara DelaTorre An analytic construction of singular solutions related to a critical Yamabe problem Comm. PDE (2020), 1784209, 26 pp. .pdf
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 .pdf
Masomeh Jamshid Nejad, Juncheng Wei Lamellar phase solutions for diblock copolymers with nonlocal diffusions Phys. D 388 (2019), 22–32 .pdf
Juncheng Wei On De Giorgi’s conjecture: recent progress and open problems Sci. China Math. 61 (2018), no. 11, 1925–1946 .pdf
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 .pdf
/ The multiplier problem of the calculus of variations for scalar ordinary differential equations Calc. Var. PDE 57 (2018), no. 2, Art. 40, 32 pp. .pdf
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. .pdf
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 .pdf
Juncheng Wei Traveling wave solutions for bistable fractional Allen–Cahn equations with a pyramidal front J. Differential Equations 262 (2017), no. 9, 4567–4609 .pdf


Accepted papers



# 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.


Preprints



# 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


Work in progress



# 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