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Hyperjacobians, determinantal ideals and weak solutions to variational problems

Published online by Cambridge University Press:  14 November 2011

Peter J. Olver
Peter J. Olver
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, U.S.A
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Synopsis

The problem of classifying homogeneous null Lagrangians satisfying an nth order divergence identity is completely solved. All such differential polynomials are affine combinations of higher order Jacobian determinants, called hyperjacobians, which can be expressed as higher dimensional determinants of higher order Jacobian matrices. Special cases, called transvectants, are of importance in classical invariant theory. Transform techniques reduce this question to the characterization of the symbolic powers of certain determinantal ideals. Applications to the proof of existence of minimizers of certain quasi-convex variational problems with weakened growth conditions are discussed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 3-4 , 1983 , pp. 317 - 340
Copyright
Copyright © Royal Society of Edinburgh 1983

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