Publications
Functional analysis
L. Korobenko, Orlicz Sobolev inequalities and the doubling condition, Annales Fennici Mathematici, 46(1), (2021), 153–161. Available as arXiv:1906.04088
L. Korobenko, D. Maldonado, and C. Rios, From Sobolev inequality to doubling, Proceedings of the AMS 143 (9), (2015), 4017-4028. Available as arXiv:1312.0277
Degenerate elliptic PDE's
L. Korobenko, E. Sawyer, Sums of squares III: hypoellipticity in the infinitely degenerate regime, submitted (2023), arXiv:2107.12451
L. Korobenko, E. Sawyer, Sums of squares II: matrix functions, Linear Algebra and its Applications 664, (2023), 264-313, arXiv:2107.12505
L. Korobenko, E. Sawyer, Sums of squares I: scalar functions, Journal of Functional Analysis, 284, (2023), 109827, arXiv:2107.12840
U. Hafeez, T. Lavier, L. Williams, and L. Korobenko, Orlicz Sobolev inequalities and the Dirichlet problem for infinitely degenerate elliptic operators, Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 82, 1-19, arXiv:2008.08263
L. Korobenko, E. Sawyer, Continuity of infinitely degenerate weak solutions via the trace method, Journal of Functional Analysis, 281(9), (2021), 109-170. Available as arXiv:2007.04878
L. Korobenko, C. Rios, E. Sawyer, R. Shen, Local boundedness, maximum principles, and continuity of solutions to infinitely degenerate elliptic equations with rough coefficients, Memoirs of the AMS 269 (2021), No. 1311. Available as arXiv:1608.01630 and arXiv:1703.00774
L. Korobenko, C. Rios, E. Sawyer, R. Shen, Local boundedness, maximum principles, and continuity of solutions to infinitely degenerate elliptic equations, preprint. Available as arXiv:1506.09203
T. Akhunov, L. Korobenko, C. Rios, Hypoellipticity for Fedii's type operators under Morimoto's logarithmic condition, Journal of Pseudo-Differential Operators and Applications 10 (3), (2019), 649-688. Available as arXiv:1711.00161
L. Korobenko, C. Rios, Hypoellipticity of certain infinitely degenerate second order operators, Journal of Mathematical Analysis and Applications 409 (2014), No. 1, 41–55. Available as arXiv:1301.2339
Stochastic processes
J. Dong, L. Korobenko, D. Sezer, A variation of Merton's corporate bond valuation model for firms with illiquid but observable assets, Quantitative Finance (2019), DOI: 10.1080/14697688.2019.1683220. Available as arXiv:1910.08641
Population dynamics
L. Korobenko, E. Braverman, On evolutionary stability of carrying capacity driven dispersal in competition with regularly diffusing populations, Journal of Mathematical Biology 69 (5), (2014), 1181-1206
L. Korobenko, M. K. Jaman and E. Braverman, Persistence and extinction in spatial models with carrying capacity driven diffusion and harvesting, Journal of Mathematical Analysis and Applications 399 (1), (2013), 352-368
L. Korobenko and E. Braverman, On logistic models with a carrying capacity dependent diffusion: stability of equilibria and coexistence with a regularly diffusing population, Nonlinear Analysis Series B: Real World Applications 13 (2012), No. 6, 2648-2658
L. Korobenko and E. Braverman, On permanence and stability of a logistic model with harvesting and a carrying capacity dependent diffusion, Journal of Nonlinear Systems and Applications 2 (2011), No. 1-2, 9-15
L. Korobenko and E. Braverman, A logistic model with a carrying capacity driven diffusion, Can. Appl. Math. Quart. 17 (2009), 85-100
Discontinuous heat equation
L. V. Korobenko, V. Zh. Sakbaev, Formulation and well-posedness of the Cauchy problem for a diffusion equation with discontinuous degenerating coefficients, Computational Mathematics and Mathematical Physics 49 (2009), no. 6, 1037-1053
L. V. Korobenko, On a description of a diffusion phenomena in discontinuous medium, Some Problems of Fundamental and Applied Mathematics (2008), 34-49 [in Russian]
L. V. Korobenko, V. Zh. Sakbaev, Solution of the diffusion equation with discontinuous coefficient on a real line, Some Problems of Fundamental and Applied Mathematics (2006), 71-85 [in Russian]
Other projects
IMUS Lecture Notes on Harmonic Analysis, Metric Spaces and PDEs, Seville 2011, edited by L. Chaffee, T. Dupuy, R. Espinola, J. Hart, A. Kairema, L. Korobenko
M. Hennessy, L. Korobenko, I. Moyles, ODE analysis of a cancer pathway, report at the 9th Annual PIMS IPSW, University of Calgary, 2009
M. Hennessy, L. Korobenko, I. Moyles, Dynamics of a large ocean vessel, report at the 9th Annual PIMS GIMMIC, University of Calgary, 2009