On the local theory of prescribed Jacobian equations | Zendy

Neil S. Trudinger | Zendy

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On the local theory of prescribed Jacobian equations

Author(s) -

Neil S. Trudinger

Publication year - 2013

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2014.34.1663

Subject(s) - jacobian matrix and determinant , convexity , generality , mathematics , scalar (mathematics) , function (biology) , variable (mathematics) , mathematical analysis , economics , geometry , management , evolutionary biology , financial economics , biology

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.

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