UAH

Craig Cowan

Assistant Professor

Address Information

Research Interests:

  • Elliptic partial differential equations
  • Regularity of solutions, Liouville type theorems.

Selected Publications

Preprints

  • C. Cowan, Regularity of stable solutions of a Lane-Emden type system. 
  • C. Cowan and M. Fazly, Regularity of the extremal solutions associated to some elliptic systems.
  • C. Cowan, Uniqueness of solutions for elliptic systems and fourth order equations involving a parameter. 

Accepted/Published

  • C. Cowan, Stability of entire solutions to supercritical elleptic problems involving advection, to appear in Nonlinear Analysis.
  • C. Cowan, Supercritical elliptic problems on a perturbation of the ball, J. Differential Equations 256 (2014), no. 3, 1250-1263.
  • C. Cowan, A Liouville theorem for a fourth order Henon equation. To appear in Advanced Nonlinear Studies.
  • C. Cowan, Liouville theorems for stable Lane-Emden systems and biharmonic problems.  Nonlinearity 26 (2013), no. 8, 2357-2371.
  • C. Cowan, N. Ghoussoub,  Regularity of semi-stable solutions to fourth order nonlinear eigenvalue problems on general domains.  Calculus of Variations and Partial Differential Equations 49 (2014), no. 1-2, 291-305.
  • C. Cowan and M. Fazly, Uniqueness of solutions for elliptic problems involving the square root of the Laplacian operator. Mathematical Research Letters 19 (2012), no. 3, 613-626.
  • C. Cowan and M. Fazly, On stable entire solutions of semi linear elliptic equations with weights. Proc. Amer. Math. Soc. 140 (2012).
  • C. Cowan, Regularity of the extremal solutions in a Gelfand systems problem. Adv. Nonlinear Stud. Vol. 11, No. 3, (2011), 695-700.
  • C. Cowan, P. Esposito and N. Ghoussoub, Regularity of extremal solutions in fourth order nonlinear Eigen value problems on general domains. Discrete Contin. Dyn. Syst. 28 (2010) no.3, 1033-1050.
  • C. Cowan, P. Esposito, N. Ghoussoub and A. Moradifam, The critical dimension for a fourth order elliptical problem with singular nonlinearity. Arch. Ration. Mech. Anal. (2009). 19 pp.
  • C. Cowan and N. Ghoussoub, Estimates on pull-in distances in microelectromechanical systems models and other nonlinear Eigenvalue problems, SIAM Journal on Mathematical Analysis, 2010, 1949-1966.
  • C. Cowan and N. Ghoussoub, Regularity of the extremal solution in a MEMS model with advection. Methods Appl. Anal. (2008) 8pp.
  • C. Cowan, Optimal Hardy inequalities for general elliptic operators with improvements. Commun. Pure Appl. Anal. (2010) 31 pp.
  • Professional Background

  • BSc, Simon Fraser University, 2004
  • MSc, Simon Fraser University, 2006
  • PhD,  University of British Columbia, 2010 
  • Postdoctoral fellow at Stanford University, August, 2010  to June, 2012