Associate Professor

Department of Mathematics

University of Manitoba

Office: 435 Machray Hall

Phone: 204-474-8707

Email : Craig.Cowan@umanitoba.ca

** Research
**

My research is in the area of nonlinear analysis and partial differential equations. I mostly concentrate on elliptic partial
differential equations.

** Opportunities For Graduate Students
**

Students with an interest in analysis and (or) differential equations are invited apply.

** Teaching,
**

Math1500_classwebpage

Math3440

Math3460

Math7460

** Preprints
**

- C. Cowan,
**Nonradial solutions of a Neumann H\'enon equation on a ball**, (2023) submitted. - A. Aghajani and C. Cowan,
**On a Brezis-Nirenberg Problem with advection**, (2022) submitted. - C. Cowan and A. Razani,
**q-Laplace equation involving the gradient on general bounded and exterior domains**, submitted (2022). - A. Aghajani and C. Cowan,
**On the regularity of extremal solutions of semilinear elliptic equations**, submitted. - C. Cowan,
**A remark on optimal H\"older continuity and dimension of the rupture set for a MEMS equation**, submitted.

**Publications**

- C. Cowan and A. Momeni,
**On supercritical elliptic problems: existence, multiplicity of positive and symmetry breaking solutions,**, Mathematische Annalen, pg 1-64, (2023), pdf. - C. Cowan,
**Supercritical problems via a fixed point argument on monotonic functions**, Nonlinear Differ. Equ. Appl. 29, 68 (2022), pdf. - C. Cowan and A. Momeni,
**Supercritical elliptic problems on nonradial domains via a nonsmooth variational approach**, Journal of Differential Equations, Volume 341, 25 December 2022, Pages 292-323, pdf. - A. Aghajani, C. Cowan and S. H. Lui,
**A nonlinear elliptic problem involving the gradient on a half space**, accepted DCDS A, (2022), pdf, submitted. - C. Cowan and A. Razani,
**Singular solutions of a H\'enon equating involving a nonlinear gradient**, accepted CPAA (2021) - A. Aghajani, C. Cowan and A. Momeni,
**The Gelfand problem on annular domains of double revolution with monotonicity**, accepted PAMS (2022)pdf - A. Aghajani and C. Cowan,
**An elliptic problem involving large advection**, accepted Potential Analysis, (2021). pdf - A. Aghajani and C. Cowan,
**A supercritical variable exponent problem**, accepted JMAA, (2021). - A. Aghajani and C. Cowan,
**Some elliptic problems involving the gradient on general bounded and exterior domains**, pdf accepted, Calc. of Variations and pde, 2021. - A. Aghajani, C. Cowan and V.D. Radulescu,
**Explicit estimates on positive supersolutions of fourth-order nonlinear elliptic equations and applications**, Journal of Differential Equations, Volume 298, 2021, Pages 323-345. - C. Cowan,
**Supercritical elliptic problems involving a Cordes like operator**, pdf, Discrete \& Continuous Dynamical Systems A, 2021, 41 (9) : 4297-4318. - C. Cowan and A. Razani,
**Singular solutions of a Lane-Emden system**, Discrete & Continuous Dynamical Systems A, 2021, 41(2): 621-656. - A. Aghajani and C. Cowan,
**A note on the nonexistence of positive supersolutions to elliptic equations with gradient terms**, Annali di Matematica 200, 125-135 (2021), pdf - C. Cowan and A. Razani,
**Singular solutions of a $p$-Laplace equation involving the gradient**, Journal of Differential Equations, Volume 269, Issue 4, 2020, Pages 3914-3942, pdf - S. Ai and C. Cowan,
**Critical elliptic equations via a dynamical system approach**, Nonlinear Analysis Volume 182, May 2019, Pages 97-112. pdf - A. Aghajani and C. Cowan,
**Explicit estimates on positive supersolutions of nonlinear elliptic equations and applications**,Volume 39, Number 5, 2731-2742, May 2019, Discrete and Continuous Dynamical Systems - Series A. pdf - A. Aghajani and C. Cowan,
**Singular solutions of elliptic equations on a perturbed cone**, Volume 266, Issue 6, 5 March 2019, Pages 3328-3366, J. Differential Equations, pdf. - C. Cowan and A. Momeni,
**A new variational principle, convexity and supercritical Neumann problems**, Trans. Amer. Math. Soc. 371 (2019), 5993-6023. pdf. - A. Aghajani and C. Cowan,
**Regularity of the extremal solutions associated to elliptic systems**, Volume 149, Issue 4August 2019 , pp. 1037-1046, The Royal Society of Edinburgh Proceedings A. - A. Aghajani, C. Cowan and S. H. Lui,
**Singular solutions of elliptic equations involving nonlinear gradient terms on perturbations of the ball**, J. Differential Equations 264 (2018) 2865-2896, pdf - A. Aghajani, C. Cowan and S. H. Lui,
**Existence and regularity of nonlinear advection problems**, Nonlinear Analysis Volume 166, January 2018, Pages 19-47, pdf. - C. Cowan, A. Momeni and L. Salimi,
**Supercritical Neumann problems via a new variational principle**, Electron. J. Differential Equations, Vol. 2017 (2017), No. 213, pp. 1-19, pdf. - S. Ai and C. Cowan,
**Perturbations of Lane-Emden and Hamilton-Jacobi equations: the full space case**, Nonlinear Analysis: Theory, Methods and Applications, Volume 151, March 2017, Pages 227-251.pdf - S. Ai and C. Cowan,
**Perturbations of Lane-Emden and Hamilton-Jacobi equations II: exterior domains**, Journal of Differential Equations Volume 260, Issue 11, 5 June 2016, Pages 8025-8050. pdf - C. Cowan,
**A short remark regarding Pohozaev type results on general domains assuming finite Morse index**, Accepted The Royal Society of Edinburgh Proceedings A, Volume 147, Issue 2 April 2017, pp. 293-297 . pdf - C. Cowan,
**Uniqueness of solutions for elliptic systems and fourth order equations involving a parameter**, CPAA, pg 519 - 533, Volume 15, Issue 2, March 2016 pdf - C. Cowan,
**Regularity of stable solutions of a Lane-Emden type system**, Methods Appl. Anal, Volume 22 (2015) Number 3, pg 301 - 312. pdf - C. Cowan and M. Fazly,
**Regularity of the extremal solutions associated to elliptic systems**, J. Differential Equations 257(2014)4087-4107, pdf - C. Cowan,
**Stability of entire solutions to supercritical elliptic problems involving advection**, Nonlinear Analysis: Theory, Methods & Applications Volume 104, July 2014, Pages 1-11. pdf - C. Cowan,
**A Liouville theorem for a fourth order Henon equation**, Advanced Nonlinear Studies 14 (2014), 737-746, pdf - C. Cowan,
**Supercritical elliptic problems on a perturbation of the ball**, J. Differential Equations 256 (2014), no. 3, 1250-1263. pdf - C. Cowan and N. Ghoussoub,
**Regularity of semi-stable solutions to fourth order nonlinear eigenvalue problems on general domains**, Calc. Var. Partial Differential Equations 49 (2014), no. 1-2, 291-305. pdf - C. Cowan,
**Liouville theorems for stable Lane-Emden systems and biharmonic problems**, Nonlinearity 26 (2013) 2357-2371. pdf - C. Cowan and M. Fazly,
**Uniqueness of solutions for a nonlocal elliptic eigenvalue problem**, Math. Res. Lett. 19 (2012), no. 03, 613-626. pdf - C. Cowan and M. Fazly,
**On stable entire solutions of semi-linear elliptic equations with weights**, Proc. Amer. Math. Soc. 140 (2012), 2003-2012. pdf - C. Cowan,
**Regularity of the extremal solutions in a Gelfand systems problem**, Adv. Nonlinear Stud. Vol. 11, No. 3, (2011), 695-700. pdf - C. Cowan, P. Esposito, N. Ghoussoub and A. Moradifam,
**The critical dimension for a fourth order elliptic problem with singular nonlinearity**, Arch. Ration. Mech. Anal. 198 (2010), no. 3, 763-787. pdf - C. Cowan and N. Ghoussoub,
**Estimates on pull-in distances in microelectrome- chanical systems models and other nonlinear eigenvalue problems**SIAM J. Math. Anal. 42 (2010), no. 5, 1949-1966. - C. Cowan, P. Esposito and N. Ghoussoub,
**Regularity of extremal solutions in fourth order nonlinear eigenvalue problems on general domains**, Discrete Contin. Dyn. Syst. 28 (2010), no. 3, 1033-1050. - C. Cowan,
**Optimal Hardy inequalities for general elliptic operators with improve- ments**Commun. Pure Appl. Anal. 9 (2010), no. 1, 109-140. pdf - C. Cowan and N. Ghoussoub,
**Regularity of the extremal solution in a MEMS model with advection**, Methods Appl. Anal. 15 (2008), no. 3, 355-360. pdf - C. Cowan,
**An elementary remark on the intersection of sets**, Real Anal. Exchange 32 (2006/07). (Work done as an undergraduate)

**Links**

Squamish Nation Art by Siobhan Joseph here.

Kayak/Paddle board rentals on Pender Island, BC.

- C. Cowan and A. Momeni,