On the local theory of prescribed Jacobian equations

Neil S. Trudinger

doi:10.3934/dcds.2014.34.1663

On the local theory of prescribed Jacobian equations

Neil S. Trudinger^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

43 Citations (Scopus)

Abstract

We develop the fundamentals of a local regularity theory for prescribed Jacobian equations which extend the corresponding results for optimal transportation equations. In this theory the cost function is extended to a generating function through dependence on an additional scalar variable. In particular we recover in this generality the local regularity theory for potentials of Ma, Trudinger and Wang, along with the subsequent development of the underlying convexity theory.

Original language	English
Pages (from-to)	1663-1681
Number of pages	19
Journal	Discrete and Continuous Dynamical Systems
Volume	34
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2014.34.1663
Publication status	Published - Apr 2014

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10.3934/dcds.2014.34.1663

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title = "On the local theory of prescribed Jacobian equations",

abstract = "We develop the fundamentals of a local regularity theory for prescribed Jacobian equations which extend the corresponding results for optimal transportation equations. In this theory the cost function is extended to a generating function through dependence on an additional scalar variable. In particular we recover in this generality the local regularity theory for potentials of Ma, Trudinger and Wang, along with the subsequent development of the underlying convexity theory.",

keywords = "Convexity, Duality, Existence and regularity, Generating function, Prescribed Jacobian equations",

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N2 - We develop the fundamentals of a local regularity theory for prescribed Jacobian equations which extend the corresponding results for optimal transportation equations. In this theory the cost function is extended to a generating function through dependence on an additional scalar variable. In particular we recover in this generality the local regularity theory for potentials of Ma, Trudinger and Wang, along with the subsequent development of the underlying convexity theory.

AB - We develop the fundamentals of a local regularity theory for prescribed Jacobian equations which extend the corresponding results for optimal transportation equations. In this theory the cost function is extended to a generating function through dependence on an additional scalar variable. In particular we recover in this generality the local regularity theory for potentials of Ma, Trudinger and Wang, along with the subsequent development of the underlying convexity theory.

KW - Convexity

KW - Duality

KW - Existence and regularity

KW - Generating function

KW - Prescribed Jacobian equations

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DO - 10.3934/dcds.2014.34.1663

M3 - Article

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VL - 34

SP - 1663

EP - 1681

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 4

ER -

On the local theory of prescribed Jacobian equations

Abstract

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