Hardy Chan

I am a current Ph.D. student at the University of British Columbia. My advisors are Prof. Nassif Ghoussoub and Prof. Juncheng Wei.

I am mainly interested in non-linear partial differential equations, whether local or non-local.

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


List of publications:
  1. (with J. Dávila, M. del Pino, Y. Liu and J. Wei) A gluing construction for fractional elliptic equations. Part II: Counterexamples of De Giorgi Conjecture for the fractional Allen--Cahn equation, in preparation.
  2. (with W. Ao, M.d.M. González and J. Wei) Bound state solutions for the supercritical fractional Schrödinger equation, preprint 2018, arXiv:1805.02915 .
  3. (with W. Ao, A. DelaTorre, M.d.M. González and J. Wei) On higher dimensional singularities for the fractional Yamabe problem: a non-local Mazzeo-Pacard program, preprint 2018, arXiv:1802.07973 .
  4. (with J. Wei) On De Giorgi’s conjecture: recent progress and open problems, accepted by Science China Mathematics.
  5. (with S. Shakerian and L.F.O. Faria) A variational problem associated to a hyperbolic Caffarelli--Kohn--Nirenberg inequality , preprint 2017, arXiv:1711.05927 .
  6. (with Y. Liu and J. Wei) A gluing construction for fractional elliptic equations. Part I: A model problem on the catenoid, preprint 2017, arXiv:1711.03215 .
  7. (with N. Ghoussoub, S. Mazumdar, S. Shakerian and L.F.O. Faria) Mass and extremals associated with the Hardy--Schrödinger operator on hyperbolic space , preprint 2017, arXiv:1710.01271 .
  8. The multiplier problem of the calculus of variations for scalar ordinary differential equations , Calc. Var. Partial Differential Equations 57 (2018), no. 2, Art. 40, 32pp.
  9. (with W. Ao, M.d.M. González and J. Wei) Existence of positive weak solutions for fractional Lane--Emden equations with prescribed singular sets , preprint 2017, submitted to CVPDE.
  10. (with J. Wei) Traveling wave solutions for bistable fractional Allen--Cahn equations with a pyramidal fornt , J. Differential Equations 262 (2017), no. 9, 4567-4609.
  11. (with W. Ao and J. Wei) Boundary concentrations on segments for the Lin-Ni-Takagi problem , accepted by Ann. Sc. Norm. Super. Pisa Cl. Sci.