Research - Scott Rodney

Publications

The weak maximum principle for solutions of degenerate elliptic equations with lower order terms.
- wuth D. Cruz-Uribe. To appear (2025)
arXiv:2512.00244 [math.AP]
Existence and Uniqueness of Solutions of Degenerate Elliptic Equations with Lower Order Terms
- with S. Cetin, D. Cruz-Uribe, F. Dal, and Y. Zeren To appear (2025)
arXiv:2507.03818 [math.AP]
Harnack inequality for degenerate elliptic equations with matrix weights.
- with G. Di Fazio, M.S. Fanciullo, and P. Zamboni Advances in Calculus of Variations, vol. 18, no. 4, (2025). https://doi.org/10.1515/acv-2024-0124
Degenerate Sobolev inequalities from the classical Sobolev inequality
- with D. Cruz-Uribe, F. Dal, and Y. Zeren Analysis and Mathematical Physics Anal.Math.Phys. 15, 75 (2025). https://doi.org/10.1007/s13324-025-01065-7
Bounded solutions of degenerate elliptic equations with an Orlicz-gain Sobolev inequality
- with D. Cruz-Uribe and S. F. MacDonald Journal to Appear. (2025)
arXiv:2412.07540 [math.AP]
Matrix Weights and Regularity for Degenerate Elliptic Equations
- with Giuseppe DiFazio, Maria Stella Fanciullo, Dario D. Monticelli, and Pietro Zamboni Nonlinear Analysis, Volume 237, (2023) https://doi.org/10.1016/j.na.2023.113363
arXiv:2302.02220 [math.AP]
Bounded Weak Solutions of p-Poisson Equations
- with Sullivan F. MacDonald Journal to Appear. (2022)
ArXiv:2210.12441 [math.AP]
Families of Young Funtions and Limits of Orlicz Norms
- with Sullivan F. MacDonald Bulletin of the Canadian Mathematical Society. (2023)
Accessible soon. arXiv: arXiv:2209.01149 [math.AP]
A Note on the Limit of Orlicz Norms
- with David Cruz-Uribe, SFO Real Anaysis Exchange (48), (2023), p. 77-82, 10.14321/realanalexch.48.1.1606864896
arXiv:2012.00707 [math.CA]
Poincaré Inequalities and Neumann Problems for the Variable Exponent Setting
- with David Cruz-Uribe, SFO and Michael Penrod Mathematics in Engineering, Vol. 4, issue 5, pp. 1-22 (2022), 10.3934/mine.2022036
ArXiv:2108.09514 [math.AP]
The Cognition of Counterexample in Mathematics Students
- with Shannon Ezzat Journal to Appear. (2021).
ArXiv:2102.05171 [math.HO]
Bounded Weak Solutions to Elliptic Equations with Data in Orlicz Spaces.
- With D. Cruz-Uribe, SFO J. Diff. Eq. Vol. 297, pp. 409-432 (2021), 10.1016/j.jde.2021.06.025,
ArXiv:2011.14491 [math.AP]
An Improved Compact Embedding Theorem for Degenerate Sobolev Spaces
- With D. D. Monticelli Le Mathematiche, Vol. LXXV, Issue I, pp. 259–275 (2020), 10.4418/2020.75.1.12
ArXiv:1908.05642 [math.AP]
Global Sobolev Inequalities and Degenerate p-Laplacian Equations
- With David Cruz-Uribe (OFS) and Emily Rosta. J. Differential Equations, Vol. 268, issue 10, pp. 6189-6210 (2019), 10.1016/j.jde.2019.11.034 .
ArXiv:1801.09610v1 [math.AP]
Poincare Inequalities and Neumann Problems for the p-Laplacian
- With David Cruz-Uribe (OFS) and Emily Rosta. Bulletin of Can. Math. Soc. Vol. 61, issue 4, pp. 738 - 753 (2018), 10.4153/CMB-2018-001-6.
ArXiv:1708.03932v1 [math.AP] .
Matrix A_p Weights, Degenerative Sobolev Spaces, and Mappings of Finite Distortion
- with David Cruz-Uribe, SFO and Kabe Moen, J. Geom. Anal. Vol. 26, issue 4, pp. 2797-2830 (2015), 10.1007/s12220-015-9649-8.
ArXiv:1505.00699 [math.AP]
Regularity Results for Weak Solutions of Elliptic PDEs Below the Natural Exponent
- with David Cruz-Uribe, SFO and Kabe Moen, Annali di Matematica Pura ed Applicata Vol. 195, issue 3, pp. 725-740 (2016), 10.1007/s10231-015-0486-y,
ArXiv:1408.6749 [math.AP]
Harnack's Inequality and Holder Continuity for Weak Solutions of Degenerate Quasilinear Equations with Rough Coefficients
- with D. D. Monticelli, and R. L. Wheeden, Nonlinear Analysis Vol. 126, pp. 69-114 (2015), 10.1016/j.na.2015.05.029,
ArXiv:1411.6976 [math.AP].
Existence and Spectral Theory for Weak Solutions of Neumann and Dirichlet Problems for Linear Degenerate Elliptic Operators with Rough Coefficients
- with D. D. Monticelli, J. Differential Equations Vol. 259, issue 8, pp. 4009-4044 (2015), 10.1016/j.jde.2015.05.018,
ArXiv:1401.4149 [math.AP].
A Compact Embedding Theorem for Generalized Sobolev Spaces
- with S-K Chua and R. L. Wheeden, Pacific Journal of Mathematics Vol. 265, no. 1, pp. 17-59 (2013), 10.2140/pjm.2013.265.17,
ArXiv:1110.6907v1 [math.AP].
Existence of Weak Solutions of Linear Subelliptic Dirichlet Problems With Rough Coefficients
- S. Rodney, Canadian Journal of Mathematics, 64, no. 6, pp. 1395-1414 (2012), 10.4153/CJM-2012-029-1
ArXiv:1108.0035 .
Boundedness of Weak Solutions of Degenerate Quasilinear Equations With Rough Coefficients
- with Dario Monticelli and Richard Wheeden 2011, Differential and Integral Equations 25, no.1-2, pp.143-200 (2011), die/1356012830
ArXiv:1106.4811
A Degenerate Sobolev Inequality for a Large Open Set in a Homogeneous Space
- S. Rodney, Rutgers University, Transactions of the American Mathematical Society 362, pp.673-685 (2010)
Existence of Weak Solutions to Subelliptic P.D.E.'s in Divergence Form and the Necessity of the Sobolev and Poincare Inequalities
- S. Rodney, McMaster University PhD Thesis 2007.

Supervised Undergraduate Research Theses

Publications