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, A. DelaTorre, M.d.M. González and J. Wei) Nonlocal ODEs, fractional gluing and higher dimensional singularities for the fractional Yamabe problem, in preparation.
  3. (with J. Wei) On De Giorgi’s conjecture: recent progress and open problems, preprint 2017.
  4. (with S. Shakerian and L.F.O. Faria) A variational problem associated to a hyperbolic Caffarelli--Kohn--Nirenberg inequality , preprint 2017, arXiv:1711.05927 .
  5. (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 .
  6. (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 .
  7. The multiplier problem of the calculus of variations for scalar ordinary differential equations , accepted by Calc. Var. Partial Differential Equations.
  8. (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.
  9. (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.
  10. (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.