Craig Cowan

Profile

Select Publications

Name: Craig Cowan

Position Title: Associate Professor

Office Phone Number: (204) 474-8707

Email: Craig.Cowan@umanitoba.ca

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)

Courses taught

MATH 1500 A06
MATH 3440 A01
MATH 8610 T10

Links

http://server.math.umanitoba.ca/~cowanct

https://scholar.google.ca/citations?user=AYcKUREAAAAJ

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.

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.