Brown University: 2007.7–
Professor: 2017.6–
Associate Professor: 2012.7–2017.6
Assistant Professor: 2007.7–2012.6
Member of the Lefschetz Center for Dynamical Systems.
University of Pennsylvania: 2010.9–2010.12
Visiting scholar (Sabbatical).
Institute for Advanced Study: 2006.9–2007.6, 2008.9–2008.12, 2021.9-2022.5
Member & Visiting Scholar.
Mathematical Sciences Research Institute: 2007.7–2007.8
Member of ”Summer Microprogram on Nonlinear Partial Differential Equations”.
University of Chicago: 2005.9–2006.8
L.E. Dickson Instructor & Research post-doctor
University of Minnesota: 2001.9–2005.8.
Research Assistant & Teaching Assistant
| Dong, Hongjie, Xu, Longjuan. "Hessian Estimates for Non-divergence form Elliptic Equations Arising from Composite Materials." Potential Analysis, 2020. |
| Dong, Hongjie, Kim, Doyoon. "L-estimates for time fractional parabolic equations in divergence form with measurable coefficients." Journal of Functional Analysis, vol. 278, no. 3, 2020, pp. 108338. |
| Dong, Hongjie, Yang, Tong, Zhong, Mingying. "Exterior Problem of the Linear Vlasov--Poisson--Boltzmann System." SIAM Journal on Mathematical Analysis, vol. 51, no. 3, 2019, pp. 1792-1823. |
| Dong, Hongjie, Xu, Longjuan. "Gradient Estimates for Divergence Form Elliptic Systems Arising from Composite Material." SIAM Journal on Mathematical Analysis, vol. 51, no. 3, 2019, pp. 2444-2478. |
| Choi, Jongkeun, Dong, Hongjie. "Gradient estimates for Stokes systems in domains." Dynamics of Partial Differential Equations, vol. 16, no. 1, 2019, pp. 1-24. |
| Choi, Jongkeun, Dong, Hongjie. "Gradient estimates for Stokes systems with Dini mean oscillation coefficients." Journal of Differential Equations, vol. 266, no. 8, 2019, pp. 4451-4509. |
| Dong, Hongjie, Zhang, Hong. "On Schauder estimates for a class of nonlocal fully nonlinear parabolic equations." Calculus of Variations and Partial Differential Equations, vol. 58, no. 2, 2019. |
| Choi, Jongkeun, None, None, Dong, Hongjie, Kim, Doyoon, None, None. "Conormal derivative problems for stationary Stokes system in Sobolev spaces." Discrete & Continuous Dynamical Systems - A, vol. 38, no. 5, 2018, pp. 2349-2374. |
| Dong, Hongjie, Jin, Tianling, Zhang, Hong. "Dini and Schauder estimates for nonlocal fully nonlinear parabolic equations with drifts." Analysis & PDE, vol. 11, no. 6, 2018, pp. 1487-1534. |
| Dong, Hongjie, Zhang, Hong. "Dini estimates for nonlocal fully nonlinear elliptic equations." Annales de l'Institut Henri Poincaré C, Analyse non linéaire, vol. 35, no. 4, 2018, pp. 971-992. |
| Dong, Hongjie, Kim, Seick. "Fundamental solutions for second-order parabolic systems with drift terms." Proceedings of the American Mathematical Society, vol. 146, no. 7, 2018, pp. 3019-3029. |
| Choi, Jongkeun, Dong, Hongjie, Kim, Doyoon. "Green Functions of Conormal Derivative Problems for Stationary Stokes System." Journal of Mathematical Fluid Mechanics, vol. 20, no. 4, 2018, pp. 1745-1769. |
| Dong, Hongjie, Gallarati, Chiara. "Higher-order elliptic and parabolic equations with VMO assumptions and general boundary conditions." Journal of Functional Analysis, vol. 274, no. 7, 2018, pp. 1993-2038. |
| Dong, Hongjie, Kim, Doyoon. "On $L_p$-estimates for elliptic and parabolic equations with $A_p$ weights." Transactions of the American Mathematical Society, vol. 370, no. 7, 2018, pp. 5081-5130. |
| Dong, Hongjie, Escauriaza, Luis, Kim, Seick. "On $$C^1$$ C 1 , $$C^2$$ C 2 , and weak type-(1, 1) estimates for linear elliptic operators: part II." Mathematische Annalen, vol. 370, no. 1-2, 2017, pp. 447-489. |
| Dong, Hongjie, Kim, Seick. "Partial Schauder Estimates for Second-Order Elliptic and Parabolic Equations: A Revisit." International Mathematics Research Notices, vol. 2019, no. 7, 2017, pp. 2085-2136. |
| Kim, Doyoon, Dong, Hongjie, Zhang, Hong. "Neumann problem for non-divergence elliptic and parabolic equations with BMO$_x$ coefficients in weighted Sobolev spaces." Discrete and Continuous Dynamical Systems, vol. 36, no. 9, 2016, pp. 4895-4914. |
| Cho, Sungwon, Dong, Hongjie, Kim, Doyoon. "Boundary Value Problems for Parabolic Operators in a Time-Varying Domain." Communications in Partial Differential Equations, vol. 40, no. 7, 2015, pp. 1282-1313. |
| Dong, Hongjie, Zhang, Hong. "Conormal problem of higher-order parabolic systems with time irregular coefficients." Trans. Amer. Math. Soc., vol. 368, no. 10, 2015, pp. 7413-7460. |
| Dong, Hongjie, Kim, Doyoon. "Elliptic and parabolic equations with measurable coefficients in weighted Sobolev spaces." Advances in Mathematics, vol. 274, 2015, pp. 681-735. |
| Ammari, H., Dong, H., Kang, H., Kim, S. "On An Elliptic Equation Arising from Photo-Acoustic Imaging in Inhomogeneous Media." International Mathematics Research Notices, 2015. |
| Dong, Hongjie, Xiong, Jingang. "Boundary Gradient Estimates for Parabolic and Elliptic Systems from Linear Laminates." International Mathematics Research Notices, vol. 2015, no. 17, 2014, pp. 7734-7756. |
| Dong, Hongjie, Gu, Xumin. "Boundary partial regularity for the high dimensional Navier–Stokes equations." Journal of Functional Analysis, vol. 267, no. 8, 2014, pp. 2606-2637. |
| Dong, Hongjie, Li, Dong. "Global $${{dot{H}^1 cap dot{H}^{-1}}}$$ H ˙ 1 ∩ H ˙ - 1 Solutions to a Logarithmically Regularized 2D Euler Equation." J. math. fluid mech., vol. 17, no. 1, 2014, pp. 1-7. |
| Dong, Hongjie, Kim, Seick. "Green's functions for parabolic systems of second order in time-varying domains." Communications on Pure and Applied Analysis, vol. 13, no. 4, 2014, pp. 1407-1433. |
| Li, Dong, Dong, Hongjie. "On a generalized maximum principle for a transport-diffusion model with $log$-modulated fractional dissipation." Discrete and Continuous Dynamical Systems, vol. 34, no. 9, 2014, pp. 3437-3454. |
| Dong, Hongjie. "On a multi-dimensional transport equation with nonlocal velocity." Advances in Mathematics, vol. 264, 2014, pp. 747-761. |
|
Dong, Hongjie, Kim, Doyoon.
"On the impossibility of |
| Dong, Hongjie, Kim, Doyoon. "Parabolic Equations in Simple Convex Polytopes with Time Irregular Coefficients." SIAM Journal on Mathematical Analysis, vol. 46, no. 3, 2014, pp. 1789-1819. |
| Dong, Hongjie, Gu, Xumin. "Partial regularity of solutions to the four-dimensional Navier-Stokes equations." Dynamics of Partial Differential Equations, vol. 11, no. 1, 2014, pp. 53-69. |
| Dong, Hongjie, Zhang, Hong. "Schauder estimates for higher-order parabolic systems with time irregular coefficients." Calculus of Variations and Partial Differential Equations, vol. 54, no. 1, 2014, pp. 47-74. |
| Dong, Hongjie, Li, Dong. "On a one-dimensional $alpha $-patch model with nonlocal drift and fractional dissipation." Trans. Amer. Math. Soc., vol. 366, no. 4, 2013, pp. 2041-2061. |
| Dong, Hongjie. "On elliptic equations in a half space or in convex wedges with irregular coefficients." Advances in Mathematics, vol. 238, 2013, pp. 24-49. |
| Dong, Hongjie, Krylov, N. V. "On the Existence of Smooth Solutions for Fully Nonlinear Parabolic Equations with Measurable “Coefficients” without Convexity Assumptions." Communications in Partial Differential Equations, vol. 38, no. 6, 2013, pp. 1038-1068. |
| Dong, Hongjie. "Gradient Estimates for Parabolic and Elliptic Systems from Linear Laminates." Archive for Rational Mechanics and Analysis, vol. 205, no. 1, 2012, pp. 119-149. |
| Dong, Hongjie, Kim, Doyoon. "On -estimates for a class of non-local elliptic equations." Journal of Functional Analysis, vol. 262, no. 3, 2012, pp. 1166-1199. |
| Dong, Hongjie, Krylov, N. V., Li, Xu. "On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains." St. Petersburg Math. J., vol. 24, no. 1, 2012, pp. 39-69. |
| Dong, Hongjie, Strain, Robert M. "On partial regularity of steady-state solutions to the 6D Navier-Stokes equations." Indiana University Mathematics Journal, vol. 61, no. 6, 2012, pp. 2211-2229. |
| Dong, H. "Parabolic equations with variably partially VMO coefficients." St. Petersburg Math. J., vol. 23, no. 3, 2012, pp. 521-539. |
| Dong, Hongjie, Kim, Doyoon. "Schauder estimates for a class of non-local elliptic equations." Discrete and Continuous Dynamical Systems, vol. 33, no. 6, 2012, pp. 2319-2347. |
| Dong, Hongjie. "Solvability of second-order equations with hierarchically partially BMO coefficients." Trans. Amer. Math. Soc., vol. 364, no. 1, 2012, pp. 493-517. |
| Cho, Sungwon, Dong, Hongjie, Kim, Seick. "Global Estimates for Green’s Matrix of Second Order Parabolic Systems with Application to Elliptic Systems in Two Dimensional Domains." Potential Analysis, vol. 36, no. 2, 2011, pp. 339-372. |
| Dong, Hongjie, Kim, Doyoon. "Global Regularity of Weak Solutions to Quasilinear Elliptic and Parabolic Equations with Controlled Growth." Communications in Partial Differential Equations, vol. 36, no. 10, 2011, pp. 1750-1777. |
| Dong, Hongjie, Kim, Doyoon. "Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains." Journal of Functional Analysis, vol. 261, no. 11, 2011, pp. 3279-3327. |
| Dong, Hongjie. "On Similarity Solutions to the Multidimensional Aggregation Equation." SIAM Journal on Mathematical Analysis, vol. 43, no. 4, 2011, pp. 1995-2008. |
| Dong, Hongjie, Kim, Doyoon. "Parabolic and Elliptic Systems in Divergence Form with Variably Partially BMO Coefficients." SIAM Journal on Mathematical Analysis, vol. 43, no. 3, 2011, pp. 1075-1098. |
| Dong, Hongjie. "The Aggregation Equation with Power-Law Kernels: Ill-Posedness, Mass Concentration and Similarity Solutions." Commun. Math. Phys., vol. 304, no. 3, 2011, pp. 649-664. |
| Dong, Hongjie, Kim, Doyoon. "L p solvability of divergence type parabolic and elliptic systems with partially BMO coefficients." Calculus of Variations and Partial Differential Equations, vol. 40, no. 3-4, 2010, pp. 357-389. |
| Dong, Hongjie, Li, Dong. "On the 2D critical and supercritical dissipative quasi-geostrophic equation in Besov spaces." Journal of Differential Equations, vol. 248, no. 11, 2010, pp. 2684-2702. |
| Dong, Hongjie, Kim, Doyoon. "On the L p -Solvability of Higher Order Parabolic and Elliptic Systems with BMO Coefficients." Archive for Rational Mechanics and Analysis, vol. 199, no. 3, 2010, pp. 889-941. |
| Dong, Hongjie, Kim, Seick. "Partial Schauder estimates for second-order elliptic and parabolic equations." Calculus of Variations and Partial Differential Equations, vol. 40, no. 3-4, 2010, pp. 481-500. |
| Dong, Hongjie, Krylov, N. V. "Second-order elliptic and parabolic equations with $B(mathbb{R}^{2}, VMO)$ coefficients." Trans. Amer. Math. Soc., vol. 362, no. 12, 2010, pp. 6477-6477. |
| Dong, Hongjie. "Solvability of parabolic equations in divergence form with partially BMO coefficients." Journal of Functional Analysis, vol. 258, no. 7, 2010, pp. 2145-2172. |
| Dong, Hongjie, Pavlović, Nataša. "A regularity criterion for the dissipative quasi-geostrophic equations." Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol. 26, no. 5, 2009, pp. 1607-1619. |
| Dong, Hongjie. "Dissipative quasi-geostrophic equations in critical Sobolev spaces: Smoothing effect and global well-posedness." Discrete and Continuous Dynamical Systems, vol. 26, no. 4, 2009, pp. 1197-1211. |
| Dong, Hongjie, Kim, Doyoon. "Elliptic Equations in Divergence Form with Partially BMO Coefficients." Archive for Rational Mechanics and Analysis, vol. 196, no. 1, 2009, pp. 25-70. |
| Dong, Hongjie, Du, Dapeng, Li, Dong. "Finite time singularities and global well-posedness for fractal Burgers equations." Indiana University Mathematics Journal, vol. 58, no. 2, 2009, pp. 807-822. |
| Dong, Hongjie, Kim, Seick. "Green’s matrices of second order elliptic systems with measurable coefficients in two dimensional domains." Trans. Amer. Math. Soc., vol. 361, no. 06, 2009, pp. 3303-3303. |
| Dong, Hongjie, Li, Dong. "Optimal local smoothing and analyticity rate estimates for the generalized Navier-Stokes equations." Communications in Mathematical Sciences, vol. 7, no. 1, 2009, pp. 67-80. |
| Dong, Hongjie, Kim, Doyoon. "Parabolic and Elliptic Systems with VMO Coefficients." Methods and Applications of Analysis, vol. 16, no. 3, 2009, pp. 365-388. |
| Dong, Hongjie, Pavlović, Nataša. "Regularity Criteria for the Dissipative Quasi-Geostrophic Equations in Hölder Spaces." Commun. Math. Phys., vol. 290, no. 3, 2009, pp. 801-812. |
| Dong, Hongjie, Du, Dapeng. "The Navier-Stokes Equations in the Critical Lebesgue Space." Commun. Math. Phys., vol. 292, no. 3, 2009, pp. 811-827. |
| Dong, Hongjie, Li, Dong. "Finite time singularities for a class of generalized surface quasi-geostrophic equations." Proceedings of the American Mathematical Society, vol. 136, no. 07, 2008, pp. 2555-2563. |
| Du, Dapeng, Dong, Hongjie. "Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space." Discrete and Continuous Dynamical Systems, vol. 21, no. 4, 2008, pp. 1095-1101. |
| Cho, Sungwon, Dong, Hongjie, Kim, Seick. "On the Green's matrices of strongly parabolic systems of second order." Indiana University Mathematics Journal, vol. 57, no. 4, 2008, pp. 1633-1678. |
| Dong, Hongjie, Kim, Seick, Safonov, Mikhail. "On Uniqueness of Boundary Blow-Up Solutions of a Class of Nonlinear Elliptic Equations." Communications in Partial Differential Equations, vol. 33, no. 2, 2008, pp. 177-188. |
| Dong, Hongjie, Li, Dong. "Spatial Analyticity of the Solutions to the Subcritical Dissipative Quasi-geostrophic Equations." Archive for Rational Mechanics and Analysis, vol. 189, no. 1, 2008, pp. 131-158. |
| Dong, Hongjie. "Well-posedness for a transport equation with nonlocal velocity." Journal of Functional Analysis, vol. 255, no. 11, 2008, pp. 3070-3097. |
| Dong, Hongjie, Krylov, N. V. "On time-inhomogeneous controlled diffusion processes in domains." The Annals of Probability, vol. 35, no. 1, 2007, pp. 206-227. |
| Dong, Hongjie, Du, Dapeng. "Partial Regularity of Solutions to the Four-Dimensional Navier-Stokes Equations at the First Blow-up Time." Commun. Math. Phys., vol. 273, no. 3, 2007, pp. 785-801. |
| Dong, Hongjie, Krylov, Nicolai V. "The Rate of Convergence of Finite-Difference Approximations for Parabolic Bellman Equations with Lipschitz Coefficients in Cylindrical Domains." Applied Mathematics and Optimization, vol. 56, no. 1, 2007, pp. 37-66. |
| Dong, Hongjie, Staubach, Wolfgang. "Unique continuation for the Schrödinger equation with gradient vector potentials." Proceedings of the American Mathematical Society, vol. 135, no. 07, 2007, pp. 2141-2150. |
| Dong, Hongjie. "Hessian Equations with Elementary Symmetric Functions." Communications in Partial Differential Equations, vol. 31, no. 7, 2006, pp. 1005-1025. |
| Dong, Hongjie, Du, Dapeng. "On the Local Smoothness of Solutions of the Navier–Stokes Equations." J. math. fluid mech., vol. 9, no. 2, 2006, pp. 139-152. |
| Dong, Hongjie. "About smoothness of solutions of the heat equations in closed, smooth space-time domains." Communications on Pure and Applied Mathematics, vol. 58, no. 6, 2005, pp. 799-820. |
| Year | Degree | Institution |
|---|---|---|
| 2005 | PhD | University of Minnesota |
| 2001 | BS | Fudan University |
NSF Grant: DMS-1600593 (P.I.), 2016.7 to 2019.6.
NSF CAREER Award: DMS-1056737 (P.I.), 2011.7 to 2016.6.
NSF Grant: DMS-0800129 (P.I.), 2008.7 to 2012.6.
MSRI Membership: 2007.7 to 2007.8.
IAS Membership: 2006 to 2007, 2008.9 to 2008.12.
Travel Grant from AMS for ICM 2006, Madrid, Spain: August 22 to 30, 2006.
Outstanding Graduate: Fudan University, 2001.
The First, Second Prizes of People's Scholarship: Fudan University, 1998 to 2001.
Meritorious Winner of Mathematical Contest in Modeling: The Consortium for Mathematics and its Applications, 2000.
Perfect Paper on the American Invitational Mathematics Examination: The Mathematical Association of America, 1997.
The First Prize of Chinese Mathematical Olympiad: rank top 4 in P.R.China, 1997.
The First, Second Prizes: in contests of Mathematics, Physics and Chemistry, 1991 to 1997.
| Name | Title |
|---|---|
| Guo, Yan | L. Herbert Ballou University Professor of Applied Mathematics |
| Yastrzhembskiy, Timur | Prager Assistant Professor of Applied Mathematics |
| APMA 0360 - Applied Partial Differential Equations I |
| APMA 1330 - Methods of Applied Mathematics |
| APMA 2110 - Real Analysis |
| APMA 2120 - Hilbert Spaces and Their Applications |
| APMA 2230 - Partial Differential Equations |
| APMA 2230 - Partial Differential Equations I |
| APMA 2240 - Partial Differential Equations |
| APMA 2812I - Topics in the Regularity Theory of PDEs |
