Tuoc Phan’s homepage
227 Ayres hall, 1403 Circle Drive
Knoxville, TN 37996
Office: 225 Ayres hall
Email: tphan2 at utk.edu
Fax: (865) - 974 - 6576
Research interests: Partial Differential Equations
v Existence uniqueness and regularity theory
nonlinear, elliptic parabolic equations and system of equations, nonlinear
p-Laplacian equations, equations with singular degenerate coefficients,
v Nonlinear dynamics in nonlinear dispersive
Asymptotical stability of solitons in Dirac equations, Klein-Gordon equations,
and Schrödinger equations.
v Optimal control and its applications in mathematical biology: Population (cells, chemical concentration) dynamics in heteronomy. My work provides potential optimal methods for treatment and managements.
Curriculum vitae: [PDF], Research statement: [PDF], Teaching statement: [PDF]
1. Liouville type theorems for 3D stationary Navier-Stokes equations in weighted mixed-norm Lebesgue spaces, 12pp., arXiv:1812.10135 [arXiv].
3. Existence uniqueness and regularity theory for elliptic equations with complex valued potentials (with G. Todorova and B. Yordanov), submitted (2018), [preprint].
1. Weighted Calderon-Zygmund estimates for weak solutions of quasi-linear degenerate elliptic equations, Potential Analysis, DOI: 10.1007/s11118-018-9737-z [Author shared link][Journal article], [arXiv].
2. Free energy in mean field of Brownian particle (with X. Chen), Discrete and Continuous Dynamical Systems – Series A, 39 (2019), no. 2, 747-769, [Journal article] [preprint].
3. Weighted W1,p-estimates for weak solutions of degenerate elliptic equations with coefficients degenerate in one variable (with Tadele Mengesha), Nonlinear Analysis, Vol. 179 (2019), p. 184-236 https://doi.org/10.1016/j.na.2018.08.012 [Journal article][arXiv].
4. Interior gradient estimates for weak solutions of quasi-linear p-Laplacian type equations, Pacific journal of Mathematics, 297-1 (2018), 195--224. DOI 10.2140/pjm.2018.297.195, [preprint] [Journal article].
5. Gradient estimates for weak solutions of linear elliptic systems with singular-degenerate coefficients (with Dat Cao and Tadele Mengesha), AMS Contemporary Mathematics, 18 pp., accepted, [preprint], [arXiv].
6. Lorentz estimates for weak solutions of quasi-linear parabolic equations with singular divergence-free drifts, Canadian Journal of Mathematics, 36pp., accepted, DOI:10.4153/CJM-2017-049-3, [preprint].
7. Weighted W1,p-estimates for weak solutions of degenerate and singular elliptic equations (with Dat Cao and Tadele Mengesha), Indiana University Mathematics Journal, Vol. 67, No. 6 (2018), 2225-2277, [arXiv] [Journal version].
8. Regularity estimates for BMO-weak solutions of quasi-linear equations with inhomogeneous boundary conditions, Nonlinear Differential Equations and Applications NoDEA, 49 pp., DOI: 10.1007/s00030-018-0501-2, [preprint][Journal version].
9. Regularity gradient estimates for weak solutions of singular quasi-linear parabolic equations, Journal of Differential Equations 263 (2017) 8329-8361, doi.org/10.1016/j.jde.2017.08.043, [Journal paper], [arXiv].
Complete list of publication: list of publication and preprints
Grants: Simons collaboration (2015-2020), grant #354889.