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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

A characterization of the weakly continuous polynomials in the method of compensated compactness


Authors: Robert C. Rogers and Blake Temple
Journal: Trans. Amer. Math. Soc. 310 (1988), 405-417
MSC: Primary 35A15; Secondary 35B99, 46N05
MathSciNet review: 965761
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Abstract: We present a sufficient condition for weak continuity in the method of compensated compactness. The condition links weak continuity to the structure of the wave cone and the characteristic set for polynomials of degree greater than two. The condition applies to all the classical examples of weakly continuous functions and generalizes the Quadratic Theorem and the Wedge Product Theorem. In fact, the condition reduces to the Legendre-Hadamard Necessary Condition when the polynomial is quadratic, and also whenever a certain orthogonality condition is satisfied. The condition is derived by isolating conditions under which the quadratic theorem can be iterated.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0965761-0
PII: S 0002-9947(1988)0965761-0
Article copyright: © Copyright 1988 American Mathematical Society