People_

Associate Professor Jiakun Liu

FAustMS

Associate Professor in the School of Mathematics and Statistics

Phone

93515772

Fax

93514534

Email

jiakun.liu@sydney.edu.au

Address

F07 - Carslaw Building

The University of Sydney

Websites

My Homepage on Google

Biographical details

Jiakun is an ARC Future Fellow in the School of Mathematics and Statistics. He obtained his BSc from Zhejiang University (ZJU) in 2006, PhD from the Australian National University (ANU) in 2010 and subsequently held a 3-year Simons Postdoctoral Fellowship at Princeton University. Upon returning to Australia in 2013, he joined the University of Wollongong (UOW) as a Lecturer, where he secured an ARC DECRA in 2014. His contributions led to promotions to Senior Lecturer in 2016 and Associate Professor in 2022. In November 2024, Jiakun joined the University of Sydney as an Associate Professor in Analysis and PDEs.

Research interests

My primary research interests are in nonlinear elliptic and parabolic partial differential equations, with applications in geometry and optimal transportation. Specifically, I focus on the regularity theory of Monge-Ampere equations, Hessian equations, and related variational problems.

Additionally, I am interested in areas of geometry and physics closely connected to these topics, such as the geometry of convex bodies, minimal surfaces, surfaces with prescribed curvatures, and geometric flows.

Publications

By Type

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Book Chapters

Zhang, J., Zhang, M., Ren, F., Liu, J. (2017). A multiagent-based domain transportation approach for optimal resource allocation in emergency management. In Quan Bai, Fenghui Ren, Katsuhide Fujita, Minjie Zhang, Takayuki Ito (Eds.), Studies in Computational Intelligence, (pp. 19-32). Singapore: Springer Verlag. [More Information]

Journals

Chen, S., Liu, J., Wang, X. (2024). C2,α regularity of free boundaries in optimal transportation. Communications on Pure and Applied Mathematics, 77(1), 731-794. [More Information]
Chen, S., Liu, J. (2024). Optimal transport problems with the squared distance cost function; [距离平方成本函数的最优传输问题]. Zhongguo Kexue. Shuxue, 54(5), 775-783. [More Information]
Clutterbuck, J., Liu, J. (2023). Preface to the Special Issue: Nonlinear PDEs and geometric analysis – Dedicated to Neil Trudinger on the occasion of his 80th birthday. Mathematics in Engineering, 5(6), 1-5. [More Information]
Chen, S., Liu, J., Wang, X. (2023). Regularity of optimal mapping between hypercubes. Advanced Nonlinear Studies, 23(1). [More Information]
Li, Q., Liu, J., Lu, J. (2022). Nonuniqueness of Solutions to the LpDual Minkowski Problem. International Mathematics Research Notices, 2022 (12), 9114-9150. [More Information]
Luo, Z., Chen, W., Lei, N., Guo, Y., Zhao, T., Liu, J., Gu, X. (2022). The Singularity Set of Optimal Transportation Maps. Computational Mathematics and Mathematical Physics, 62(8), 1313-1330. [More Information]
Zhang, J., Zhang, M., Ren, F., Liu, J. (2021). An Innovation Approach for Optimal Resource Allocation in Emergency Management. IEEE Transactions on Computers, , 1-1. [More Information]
Chen, S., Liu, J., Wang, X. (2021). Global regularity for the Monge-Ampère equation with natural boundary condition. Annals of Mathematics, 194(3), 745-793. [More Information]
Liu, J. (2021). Interior C2 estimate for monge-ampère equation in dimension two. Proceedings of the American Mathematical Society, 149(6), 2479-2486. [More Information]
Liu, J., Wang, X. (2021). Light Refraction is Nonlinear Optimisation. Journal of Mathematical Study, 54(2), 142-163. [More Information]
Huang, Y., Liu, J. (2021). Noncompact lp-minkowski problems. Indiana University Mathematics Journal, 70(3), 855-880. [More Information]
Liu, J., Loeper, G. (2020). Optimal transport with discrete long-range mean-field interactions. Bulletin of Mathematical Sciences, 10(2). [More Information]
Du, K., Liu, J., Zhang, F. (2020). Stochastic hölder continuity of random fields governed by a system of stochastic PDEs. l' Institut Henri Poincare. Annales (B). Probabilites et Statistiques, 56(2), 1230-1250. [More Information]
Chen, S., Huang, Y., Li, Q., Liu, J. (2020). The Lp-Brunn-Minkowski inequality for p < 1. Advances in Mathematics, 368. [More Information]
Khanh, T., Liu, J., Thuc, P. (2019). Bergman–Toeplitz operators on fat hartogs triangles. Proceedings of the American Mathematical Society, 147(1), 327-338. [More Information]
Khanh, T., Liu, J., Thuc, P. (2019). Bergman–Toeplitz operators on weakly pseudoconvex domains. Mathematische Zeitschrift, 291(2024-01-02 00:00:00), 591-607. [More Information]
Chen, S., Liu, J., Wang, X. (2019). Global regularity of optimal mappings in non-convex domains. Science China Mathematics, 62(11), 2057-2072. [More Information]
Du, K., Liu, J. (2019). On the cauchy problem for stochastic parabolic equations in hölder spaces. Transactions of the American Mathematical Society, 371(4), 2643-2664. [More Information]
Li, Y., Liu, J., Nguyen, L. (2017). A degree theory for second order nonlinear elliptic operators with nonlinear oblique boundary conditions. Journal of Fixed Point Theory and Applications, 19(1), 853-876. [More Information]
Du, K., Liu, J. (2016). A Schauder estimate for stochastic PDEs. Academie des Sciences. Comptes Rendus. Mathematique, 354(4), 371-375. [More Information]
Liu, J., Trudinger, N. (2016). On the classical solvability of near field reflector problems. Discrete and Continuous Dynamical Systems - Series A, 36(2), 895-916. [More Information]
Huang, Y., Jiang, F., Liu, J. (2015). Boundary C2,α estimates for Monge-Ampère type equations. Advances in Mathematics, 281, 706-733. [More Information]
Liu, J., Trudinger, N., Wang, X. (2015). On Asymptotic Behaviour and W 2, p Regularity of Potentials in Optimal Transportation. Archive for Rational Mechanics and Analysis, 215(3), 867-905. [More Information]
Huang, Y., Liu, J., Xu, L. (2015). On the uniqueness of Lp-Minkowski problems: The constant p-curvature case in R3. Advances in Mathematics, 281, 906-927. [More Information]
Liu, J., Zhou, B. (2013). An obstacle problem for a class of Monge-Ampère type functionals. Journal of Differential Equations, 254(3), 1306-1325. [More Information]
Liu, J. (2013). Light reflection is nonlinear optimization. Calculus of Variations and Partial Differential Equations, 46(2024-03-04 00:00:00), 861-878. [More Information]
Zeng, R., Liu, J., Du, G., Li, W., Wang, J., Horvat, J., Dou, S. (2012). Magnetic and superconducting properties of spin-fluctuation-limited superconducting nanoscale VN x. Journal of Applied Physics, 111(7). [More Information]
Liu, J. (2011). Regularity of Monge-Ampère equations in optimal transportation. Bulletin of the Australian Mathematical Society, 83(1), 173-176. [More Information]
Liu, J., Trudinger, N. (2010). On Pogorelov estimates for Monge-Ampère type equations. Discrete and Continuous Dynamical Systems - Series A, 28(3), 1121-1135. [More Information]
Liu, J. (2009). Hölder regularity of optimal mappings in optimal transportation. Calculus of Variations and Partial Differential Equations, 34(4), 435-451. [More Information]
Liu, J., Trudinger, N., Wang, X. (2009). Interior C2,α regularity for potential functions in optimal transportation. Communications in Partial Differential Equations, 35(1), 165-184. [More Information]

show 28 more

Conferences

Zhang, J., Zhang, M., Ren, F., Liu, J. (2016). A decentralised multi-agent system for emergency resource allocation in metropolitan regions (demonstration). 15th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2016), Singapore: International Foundation for Autonomous Agents and Multiagent Systems.
Zhang, J., Zhang, M., Ren, F., Liu, J. (2016). Enable efficient resource deployment in multiple concurrent emergency events through a decentralised MAS. 29th Australasian Joint Conference on Artificial Intelligence (AI 2016), Cham: Springer. [More Information]

By Year

Expand all

2024

Chen, S., Liu, J., Wang, X. (2024). C2,α regularity of free boundaries in optimal transportation. Communications on Pure and Applied Mathematics, 77(1), 731-794. [More Information]
Chen, S., Liu, J. (2024). Optimal transport problems with the squared distance cost function; [距离平方成本函数的最优传输问题]. Zhongguo Kexue. Shuxue, 54(5), 775-783. [More Information]

2023

Clutterbuck, J., Liu, J. (2023). Preface to the Special Issue: Nonlinear PDEs and geometric analysis – Dedicated to Neil Trudinger on the occasion of his 80th birthday. Mathematics in Engineering, 5(6), 1-5. [More Information]
Chen, S., Liu, J., Wang, X. (2023). Regularity of optimal mapping between hypercubes. Advanced Nonlinear Studies, 23(1). [More Information]

2022

Li, Q., Liu, J., Lu, J. (2022). Nonuniqueness of Solutions to the LpDual Minkowski Problem. International Mathematics Research Notices, 2022 (12), 9114-9150. [More Information]
Luo, Z., Chen, W., Lei, N., Guo, Y., Zhao, T., Liu, J., Gu, X. (2022). The Singularity Set of Optimal Transportation Maps. Computational Mathematics and Mathematical Physics, 62(8), 1313-1330. [More Information]

2021

Zhang, J., Zhang, M., Ren, F., Liu, J. (2021). An Innovation Approach for Optimal Resource Allocation in Emergency Management. IEEE Transactions on Computers, , 1-1. [More Information]
Chen, S., Liu, J., Wang, X. (2021). Global regularity for the Monge-Ampère equation with natural boundary condition. Annals of Mathematics, 194(3), 745-793. [More Information]
Liu, J. (2021). Interior C2 estimate for monge-ampère equation in dimension two. Proceedings of the American Mathematical Society, 149(6), 2479-2486. [More Information]
Liu, J., Wang, X. (2021). Light Refraction is Nonlinear Optimisation. Journal of Mathematical Study, 54(2), 142-163. [More Information]
Huang, Y., Liu, J. (2021). Noncompact lp-minkowski problems. Indiana University Mathematics Journal, 70(3), 855-880. [More Information]

show 2 more

2020

Liu, J., Loeper, G. (2020). Optimal transport with discrete long-range mean-field interactions. Bulletin of Mathematical Sciences, 10(2). [More Information]
Du, K., Liu, J., Zhang, F. (2020). Stochastic hölder continuity of random fields governed by a system of stochastic PDEs. l' Institut Henri Poincare. Annales (B). Probabilites et Statistiques, 56(2), 1230-1250. [More Information]
Chen, S., Huang, Y., Li, Q., Liu, J. (2020). The Lp-Brunn-Minkowski inequality for p < 1. Advances in Mathematics, 368. [More Information]

2019

Khanh, T., Liu, J., Thuc, P. (2019). Bergman–Toeplitz operators on fat hartogs triangles. Proceedings of the American Mathematical Society, 147(1), 327-338. [More Information]
Khanh, T., Liu, J., Thuc, P. (2019). Bergman–Toeplitz operators on weakly pseudoconvex domains. Mathematische Zeitschrift, 291(2024-01-02 00:00:00), 591-607. [More Information]
Chen, S., Liu, J., Wang, X. (2019). Global regularity of optimal mappings in non-convex domains. Science China Mathematics, 62(11), 2057-2072. [More Information]
Du, K., Liu, J. (2019). On the cauchy problem for stochastic parabolic equations in hölder spaces. Transactions of the American Mathematical Society, 371(4), 2643-2664. [More Information]

show 1 more

2017

Li, Y., Liu, J., Nguyen, L. (2017). A degree theory for second order nonlinear elliptic operators with nonlinear oblique boundary conditions. Journal of Fixed Point Theory and Applications, 19(1), 853-876. [More Information]
Zhang, J., Zhang, M., Ren, F., Liu, J. (2017). A multiagent-based domain transportation approach for optimal resource allocation in emergency management. In Quan Bai, Fenghui Ren, Katsuhide Fujita, Minjie Zhang, Takayuki Ito (Eds.), Studies in Computational Intelligence, (pp. 19-32). Singapore: Springer Verlag. [More Information]

2016

Zhang, J., Zhang, M., Ren, F., Liu, J. (2016). A decentralised multi-agent system for emergency resource allocation in metropolitan regions (demonstration). 15th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2016), Singapore: International Foundation for Autonomous Agents and Multiagent Systems.
Du, K., Liu, J. (2016). A Schauder estimate for stochastic PDEs. Academie des Sciences. Comptes Rendus. Mathematique, 354(4), 371-375. [More Information]
Zhang, J., Zhang, M., Ren, F., Liu, J. (2016). Enable efficient resource deployment in multiple concurrent emergency events through a decentralised MAS. 29th Australasian Joint Conference on Artificial Intelligence (AI 2016), Cham: Springer. [More Information]
Liu, J., Trudinger, N. (2016). On the classical solvability of near field reflector problems. Discrete and Continuous Dynamical Systems - Series A, 36(2), 895-916. [More Information]

show 1 more

2015

Huang, Y., Jiang, F., Liu, J. (2015). Boundary C2,α estimates for Monge-Ampère type equations. Advances in Mathematics, 281, 706-733. [More Information]
Liu, J., Trudinger, N., Wang, X. (2015). On Asymptotic Behaviour and W 2, p Regularity of Potentials in Optimal Transportation. Archive for Rational Mechanics and Analysis, 215(3), 867-905. [More Information]
Huang, Y., Liu, J., Xu, L. (2015). On the uniqueness of Lp-Minkowski problems: The constant p-curvature case in R3. Advances in Mathematics, 281, 906-927. [More Information]

2013

Liu, J., Zhou, B. (2013). An obstacle problem for a class of Monge-Ampère type functionals. Journal of Differential Equations, 254(3), 1306-1325. [More Information]
Liu, J. (2013). Light reflection is nonlinear optimization. Calculus of Variations and Partial Differential Equations, 46(2024-03-04 00:00:00), 861-878. [More Information]

2012

Zeng, R., Liu, J., Du, G., Li, W., Wang, J., Horvat, J., Dou, S. (2012). Magnetic and superconducting properties of spin-fluctuation-limited superconducting nanoscale VN x. Journal of Applied Physics, 111(7). [More Information]

2011

Liu, J. (2011). Regularity of Monge-Ampère equations in optimal transportation. Bulletin of the Australian Mathematical Society, 83(1), 173-176. [More Information]

2010

Liu, J., Trudinger, N. (2010). On Pogorelov estimates for Monge-Ampère type equations. Discrete and Continuous Dynamical Systems - Series A, 28(3), 1121-1135. [More Information]

2009

Liu, J. (2009). Hölder regularity of optimal mappings in optimal transportation. Calculus of Variations and Partial Differential Equations, 34(4), 435-451. [More Information]
Liu, J., Trudinger, N., Wang, X. (2009). Interior C2,α regularity for potential functions in optimal transportation. Communications in Partial Differential Equations, 35(1), 165-184. [More Information]

Selected Grants

2024