On Asymptotic Behaviour and W 2, p Regularity of Potentials in Optimal Transportation
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| 024 | 7 | 0 | |a 10.1007/s00205-014-0797-y |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-014-0797-y | ||
| 245 | 0 | 0 | |a On Asymptotic Behaviour and W 2, p Regularity of Potentials in Optimal Transportation |h [Elektronische Daten] |c [Jiakun Liu, Neil Trudinger, Xu-Jia Wang] |
| 520 | 3 | |a In this paper we study local properties of cost and potential functions in optimal transportation. We prove that in a proper normalization process, the cost function is uniformly smooth and converges locally smoothly to a quadratic cost x · y, while the potential function converges to a quadratic function. As applications we obtain the interior W 2, p estimates and sharp C 1, α estimates for the potentials, which satisfy a Monge-Ampère type equation. The W 2, p estimate was previously proved by Caffarelli for the quadratic transport cost and the associated standard Monge-Ampère equation. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2014 | ||
| 700 | 1 | |a Liu |D Jiakun |u Institute for Mathematics and its Applications, School of Mathematics and Applied Statistics, University of Wollongong, 2522, Wollongong, NSW, Australia |4 aut | |
| 700 | 1 | |a Trudinger |D Neil |u Centre for Mathematics and Its Applications, The Australian National University, 0200, Canberra, ACT, Australia |4 aut | |
| 700 | 1 | |a Wang |D Xu-Jia |u Centre for Mathematics and Its Applications, The Australian National University, 0200, Canberra, ACT, Australia |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 215/3(2015-03-01), 867-905 |x 0003-9527 |q 215:3<867 |1 2015 |2 215 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-014-0797-y |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-014-0797-y |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Liu |D Jiakun |u Institute for Mathematics and its Applications, School of Mathematics and Applied Statistics, University of Wollongong, 2522, Wollongong, NSW, Australia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Trudinger |D Neil |u Centre for Mathematics and Its Applications, The Australian National University, 0200, Canberra, ACT, Australia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Wang |D Xu-Jia |u Centre for Mathematics and Its Applications, The Australian National University, 0200, Canberra, ACT, Australia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 215/3(2015-03-01), 867-905 |x 0003-9527 |q 215:3<867 |1 2015 |2 215 |o 205 | ||