On the local theory of prescribed Jacobian equations revisited
In this paper we revisit our previous study of the local theory of prescribed Jacobian equations associated with generating functions, which are extensions of cost functions in the theory of optimal transportation. In particular, as foreshadowed in the earlier work, we provide details pertaining to...
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doaj-63e181673c2f4e20a038572bc61c98792021-03-24T01:34:52ZengAIMS PressMathematics in Engineering2640-35012021-03-013611710.3934/mine.2021048On the local theory of prescribed Jacobian equations revisitedNeil S. Trudinger0Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, AustraliaIn this paper we revisit our previous study of the local theory of prescribed Jacobian equations associated with generating functions, which are extensions of cost functions in the theory of optimal transportation. In particular, as foreshadowed in the earlier work, we provide details pertaining to the relaxation of a monotonicity condition in the underlying convexity theory and the consequent classical regularity. Taking advantage of recent work of Kitagawa and Guillen, we also extend our classical regularity theory to the weak form A3w of the critical matrix convexity conditions.http://www.aimspress.com/article/doi/10.3934/mine.2021048?viewType=HTMLprescribed jacobian equationsgenerating functionsconvexity theoryexistence and regularity |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Neil S. Trudinger |
spellingShingle |
Neil S. Trudinger On the local theory of prescribed Jacobian equations revisited Mathematics in Engineering prescribed jacobian equations generating functions convexity theory existence and regularity |
author_facet |
Neil S. Trudinger |
author_sort |
Neil S. Trudinger |
title |
On the local theory of prescribed Jacobian equations revisited |
title_short |
On the local theory of prescribed Jacobian equations revisited |
title_full |
On the local theory of prescribed Jacobian equations revisited |
title_fullStr |
On the local theory of prescribed Jacobian equations revisited |
title_full_unstemmed |
On the local theory of prescribed Jacobian equations revisited |
title_sort |
on the local theory of prescribed jacobian equations revisited |
publisher |
AIMS Press |
series |
Mathematics in Engineering |
issn |
2640-3501 |
publishDate |
2021-03-01 |
description |
In this paper we revisit our previous study of the local theory of prescribed Jacobian equations associated with generating functions, which are extensions of cost functions in the theory of optimal transportation. In particular, as foreshadowed in the earlier work, we provide details pertaining to the relaxation of a monotonicity condition in the underlying convexity theory and the consequent classical regularity. Taking advantage of recent work of Kitagawa and Guillen, we also extend our classical regularity theory to the weak form A3w of the critical matrix convexity conditions. |
topic |
prescribed jacobian equations generating functions convexity theory existence and regularity |
url |
http://www.aimspress.com/article/doi/10.3934/mine.2021048?viewType=HTML |
work_keys_str_mv |
AT neilstrudinger onthelocaltheoryofprescribedjacobianequationsrevisited |
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1724205256110243840 |