Craig Cowan
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

  1. A. Aghajani and C. Cowan, Nonradial solutions of a super critical elliptic problem with supercritical drift , submitted (2024).

  2. A. Aghajani and C. Cowan, Positive nonradial solutions of an elliptic equation with critical advection term, submitted (2024).

  3. A. Aghajani and C. Cowan, A supercritical H\'enon equation on a cylinder, submitted (2024).

  4. Craig Cowan, Mohammad El Smaily and Pierre Aime Feulefack, Existence and regularity results for a Neumann problem with mixed local and nonlocal diffusion Neumann local nonlocal, submitted (2024).

  5. C. Cowan, M. El Smaily and P.A. Feulefack, The principal eigenvalue of a mixed local and nonlocal operator with drift, submitted (2024).

  6. A. Aghajani and C. Cowan, On a Brezis-Nirenberg Problem with advection, (2022) submitted.

  7. A. Aghajani and C. Cowan, On the regularity of extremal solutions of semilinear elliptic equations, submitted.

  8. C. Cowan, A remark on optimal H\"older continuity and dimension of the rupture set for a MEMS equation, submitted.

    Publications

    1. C. Cowan, Nonradial solutions of a Neumann H\'enon equation on a ball, accepted Proceedings AMS (2024).

    2. C. Cowan and A. Razani, q-Laplace equation involving the gradient on general bounded and exterior domains,Nonlinear Differ. Equ. Appl. 31, 6 (2024).

    3. C. Cowan and A. Momeni, On supercritical elliptic problems: existence, multiplicity of positive and symmetry breaking solutions,, Mathematische Annalen, pg 1-64, (2023), pdf.

    4. C. Cowan, Supercritical problems via a fixed point argument on monotonic functions, Nonlinear Differ. Equ. Appl. 29, 68 (2022), pdf.

    5. 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.

    6. 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.

    7. C. Cowan and A. Razani, Singular solutions of a H\'enon equating involving a nonlinear gradient , accepted CPAA (2021)

    8. A. Aghajani, C. Cowan and A. Momeni, The Gelfand problem on annular domains of double revolution with monotonicity , accepted PAMS (2022)pdf

    9. A. Aghajani and C. Cowan, An elliptic problem involving large advection, accepted Potential Analysis, (2021). pdf

    10. A. Aghajani and C. Cowan, A supercritical variable exponent problem, accepted JMAA, (2021).

    11. 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.

    12. 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.

    13. C. Cowan, Supercritical elliptic problems involving a Cordes like operator, pdf, Discrete \& Continuous Dynamical Systems A, 2021, 41 (9) : 4297-4318.

    14. C. Cowan and A. Razani, Singular solutions of a Lane-Emden system, Discrete & Continuous Dynamical Systems A, 2021, 41(2): 621-656.

    15. 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

    16. 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

    17. S. Ai and C. Cowan, Critical elliptic equations via a dynamical system approach, Nonlinear Analysis Volume 182, May 2019, Pages 97-112. pdf

    18. 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

    19. 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.

    20. C. Cowan and A. Momeni, A new variational principle, convexity and supercritical Neumann problems, Trans. Amer. Math. Soc. 371 (2019), 5993-6023. pdf.

    21. 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.

    22. 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

    23. 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.

    24. 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.

    25. 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

    26. 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

    27. 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

    28. 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

    29. C. Cowan, Regularity of stable solutions of a Lane-Emden type system, Methods Appl. Anal, Volume 22 (2015) Number 3, pg 301 - 312. pdf

    30. C. Cowan and M. Fazly, Regularity of the extremal solutions associated to elliptic systems, J. Differential Equations 257(2014)4087-4107, pdf

    31. 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

    32. C. Cowan, A Liouville theorem for a fourth order Henon equation, Advanced Nonlinear Studies 14 (2014), 737-746, pdf

    33. C. Cowan, Supercritical elliptic problems on a perturbation of the ball, J. Differential Equations 256 (2014), no. 3, 1250-1263. pdf

    34. 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

    35. C. Cowan, Liouville theorems for stable Lane-Emden systems and biharmonic problems, Nonlinearity 26 (2013) 2357-2371. pdf

    36. C. Cowan and M. Fazly, Uniqueness of solutions for a nonlocal elliptic eigenvalue problem, Math. Res. Lett. 19 (2012), no. 03, 613-626. pdf

    37. 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

    38. C. Cowan, Regularity of the extremal solutions in a Gelfand systems problem, Adv. Nonlinear Stud. Vol. 11, No. 3, (2011), 695-700. pdf

    39. 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

    40. 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.

    41. 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.

    42. C. Cowan, Optimal Hardy inequalities for general elliptic operators with improve- ments Commun. Pure Appl. Anal. 9 (2010), no. 1, 109-140. pdf

    43. 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

    44. C. Cowan, An elementary remark on the intersection of sets, Real Anal. Exchange 32 (2006/07). (Work done as an undergraduate)

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