Research and Teaching Interests
Partial differential equations
Education
M.Sc. Simon Fraser University
Ph.D. University of British Columbia
Current graduate students
- Farzaneh Nikbakhtsarvestani (Ph.D.)
- Lubana Yasmin (M.Sc. Thesis)
- Aidin Zaherparandaz (M.Sc. Thesis)
Select publications
- Aghajani, A.; Cowan, C. and Lui, S. H. (2018). Existence and regularity of nonlinear advection problems. Nonlinear Anal. 166, 19–47.
- Aghajani, A.; Cowan, C. and Lui, S. H. (2018). Singular solutions of elliptic equations involving nonlineargradient terms on perturbations of the ball. J. Differential Equations 264 (4), 2865–2896.
- Ai, Shangbing and Cowan, Craig (2017). Perturbations of Lane-Emden and Hamilton-Jacobi equations: the full space case. Nonlinear Anal. 151, 227–251.
- Cowan, Craig (2017). A short remark regarding Pohozaev-type results on general domains assuming finite Morse index. Proc. Roy. Soc. Edinburgh Sect. A 147 (2), 293–297.
- Cowan, Craig; Moameni, Abbas and Salimi, Leila (2017). Existence of solutions to supercritical Neumann problems via a new variational principle. Electron. J. Differential Equations, Paper No. 213, 19.
- Ai, Shangbing and Cowan, Craig (2016). Perturbations of Lane-Emden and Hamilton-Jacobi equations II: Exterior domains. J. Differential Equations 260 (11), 8025–8050.
- Cowan, Craig (2016). Uniqueness of solutions for elliptic systems and fourth order equations involving a parameter. Commun. Pure Appl. Anal. 15 (2), 519–533.
- Cowan, Craig (2015). Regularity of stable solutions of a Lane-Emden type system. Methods Appl. Anal. 22 (3), 301–311.
- Cowan, Craig (2014). A Liouville theorem for a fourth order Hénon equation. Adv. Nonlinear Stud. 14(3), 767–776.
- Cowan, Craig (2014). Stability of entire solutions to supercritical elliptic problems involving advection. Nonlinear Anal. 104, 1–11.
- Cowan, Craig (2014). Supercritical elliptic problems on a perturbation of the ball. J. Differential Equations 256 (3), 1250–1263.
- Cowan, Craig and Fazly, Mostafa (2014). Regularity of the extremal solutions associated to elliptic systems. J. Differential Equations 257 (11), 4087–4107.
- Cowan, Craig and Ghoussoub, Nassif (2014). Regularity of semi-stable solutions to fourth order nonlinear eigenvalue problems on general domains. Calc. Var. Partial Differential Equations 49 (1-2), 291–305.
- Cowan, Craig (2013). Liouville theorems for stable Lane-Emden systems with biharmonic problems.Nonlinearity 26 (8), 2357–2371.
- Cowan, Craig and Fazly, Mostafa (2012). On stable entire solutions of semi-linear elliptic equations with weights. Proc. Amer. Math. Soc. 140 (6), 2003–2012.
- Cowan, Craig and Fazly, Mostafa (2012). Uniqueness of solutions for a nonlocal elliptic eigenvalue problem. Math. Res. Lett. 19 (3), 613–626.
- Cowan, Craig (2011). Regularity of the extremal solutions in a Gelfand system problem. Adv. Nonlinear Stud. 11 (3), 695–700.
- Cowan, Craig (2010). Optimal Hardy inequalities for general elliptic operators with improvements.Commun. Pure Appl. Anal. 9 (1), 109–140.
- Cowan, Craig; Esposito, Pierpaolo and Ghoussoub, Nassif (2010). Regularity of extremal solutions in fourth order nonlinear eigenvalue problems on general domains. Discrete Contin. Dyn. Syst. 28 (3), 1033–1050.
- Cowan, Craig; Esposito, Pierpaolo and Ghoussoub, Nassif and Moradifam, Amir (2010). The critical dimension for a fourth order elliptic problem with singular nonlinearity. Arch. Ration. Mech. Anal. 198(3), 763–787.
- Cowan, Craig and Ghoussoub, Nassif (2010). Estimates on pull-in distances in microelectromechanical systems models and other nonlinear eigenvalue problems. SIAM J. Math. Anal. 42 (5), 1949–1966.
- Cowan, Craig and Ghoussoub, Nassif (2008). Regularity of the extremal solution in a MEMS model with advection. Methods Appl. Anal. 15 (3), 355–360.
- Cowan, Craig (2006/07). An elementary remark on the intersection of sets. Real Anal. Exchange 32 (1), 221–223.
Courses taught
- MATH 1500 A06
- MATH 3440 A01
- MATH 8610 T10