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From Frank Ramsey to René Thom: A classical problem in the calculus of variations leading to an implicit differential equation
On Pogorelov estimates for Monge-Ampère type equations
1. | Centre for Mathematics and Its Applications, The Australian National University, Canberra, ACT 0200, Australia |
2. | Centre for Mathematics and Its Applications, the Australian National University, Canberra, ACT 0200, Australia |
[1] |
Gershon Wolansky. Limit theorems for optimal mass transportation and applications to networks. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 365-374. doi: 10.3934/dcds.2011.30.365 |
[2] |
A. Daducci, A. Marigonda, G. Orlandi, R. Posenato. Neuronal Fiber--tracking via optimal mass transportation. Communications on Pure and Applied Analysis, 2012, 11 (5) : 2157-2177. doi: 10.3934/cpaa.2012.11.2157 |
[3] |
Alexander V. Kolesnikov. Hessian metrics, $CD(K,N)$-spaces, and optimal transportation of log-concave measures. Discrete and Continuous Dynamical Systems, 2014, 34 (4) : 1511-1532. doi: 10.3934/dcds.2014.34.1511 |
[4] |
Luca Di Persio, Giacomo Ziglio. Gaussian estimates on networks with applications to optimal control. Networks and Heterogeneous Media, 2011, 6 (2) : 279-296. doi: 10.3934/nhm.2011.6.279 |
[5] |
David Kinderlehrer, Adrian Tudorascu. Transport via mass transportation. Discrete and Continuous Dynamical Systems - B, 2006, 6 (2) : 311-338. doi: 10.3934/dcdsb.2006.6.311 |
[6] |
Gershon Kresin, Vladimir Maz’ya. Optimal estimates for the gradient of harmonic functions in the multidimensional half-space. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 425-440. doi: 10.3934/dcds.2010.28.425 |
[7] |
Roberta Bosi, Jean Dolbeault, Maria J. Esteban. Estimates for the optimal constants in multipolar Hardy inequalities for Schrödinger and Dirac operators. Communications on Pure and Applied Analysis, 2008, 7 (3) : 533-562. doi: 10.3934/cpaa.2008.7.533 |
[8] |
Xiaoping Zhai, Yongsheng Li. Global large solutions and optimal time-decay estimates to the Korteweg system. Discrete and Continuous Dynamical Systems, 2021, 41 (3) : 1387-1413. doi: 10.3934/dcds.2020322 |
[9] |
G.S. Liu, J.Z. Zhang. Decision making of transportation plan, a bilevel transportation problem approach. Journal of Industrial and Management Optimization, 2005, 1 (3) : 305-314. doi: 10.3934/jimo.2005.1.305 |
[10] |
Vladimir Gaitsgory, Ilya Shvartsman. Linear programming estimates for Cesàro and Abel limits of optimal values in optimal control problems. Discrete and Continuous Dynamical Systems - B, 2022, 27 (3) : 1591-1610. doi: 10.3934/dcdsb.2021102 |
[11] |
Lorenzo Brasco, Filippo Santambrogio. An equivalent path functional formulation of branched transportation problems. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 845-871. doi: 10.3934/dcds.2011.29.845 |
[12] |
Jaimie W. Lien, Vladimir V. Mazalov, Jie Zheng. Pricing equilibrium of transportation systems with behavioral commuters. Journal of Dynamics and Games, 2020, 7 (4) : 335-350. doi: 10.3934/jdg.2020026 |
[13] |
Ş. İlker Birbil, Kerem Bülbül, J. B. G. Frenk, H. M. Mulder. On EOQ cost models with arbitrary purchase and transportation costs. Journal of Industrial and Management Optimization, 2015, 11 (4) : 1211-1245. doi: 10.3934/jimo.2015.11.1211 |
[14] |
Jun Pei, Panos M. Pardalos, Xinbao Liu, Wenjuan Fan, Shanlin Yang, Ling Wang. Coordination of production and transportation in supply chain scheduling. Journal of Industrial and Management Optimization, 2015, 11 (2) : 399-419. doi: 10.3934/jimo.2015.11.399 |
[15] |
Niklas Behringer. Improved error estimates for optimal control of the Stokes problem with pointwise tracking in three dimensions. Mathematical Control and Related Fields, 2021, 11 (2) : 313-328. doi: 10.3934/mcrf.2020038 |
[16] |
Yi Cao, Dong Li, Lihe Wang. The optimal weighted $W^{2, p}$ estimates of elliptic equation with non-compatible conditions. Communications on Pure and Applied Analysis, 2011, 10 (2) : 561-570. doi: 10.3934/cpaa.2011.10.561 |
[17] |
Konstantinos Chrysafinos, Efthimios N. Karatzas. Symmetric error estimates for discontinuous Galerkin approximations for an optimal control problem associated to semilinear parabolic PDE's. Discrete and Continuous Dynamical Systems - B, 2012, 17 (5) : 1473-1506. doi: 10.3934/dcdsb.2012.17.1473 |
[18] |
Xinghong Pan, Jiang Xu. Global existence and optimal decay estimates of the compressible viscoelastic flows in $ L^p $ critical spaces. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 2021-2057. doi: 10.3934/dcds.2019085 |
[19] |
Litan Yan, Xiuwei Yin. Optimal error estimates for fractional stochastic partial differential equation with fractional Brownian motion. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 615-635. doi: 10.3934/dcdsb.2018199 |
[20] |
Dominik Hafemeyer, Florian Mannel, Ira Neitzel, Boris Vexler. Finite element error estimates for one-dimensional elliptic optimal control by BV-functions. Mathematical Control and Related Fields, 2020, 10 (2) : 333-363. doi: 10.3934/mcrf.2019041 |
2020 Impact Factor: 1.392
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