Preprint 29/1999

Rank-one convexity implies quasiconvexity on diagonal matrices

Stefan Müller

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Submission date: 02. May. 1999
Pages: 12
published in: International mathematics research notices, 1999 (1999) 20, p. 1087-1095 
MSC-Numbers: 49J45, 42C15, 35B35
Keywords and phrases: compensated compactness, quasiconvexity, wavelets, haar basis, riesz transform
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We prove a conjecture of Tartar regarding weak lower semicontinuity of functionals on sequences tex2html_wrap_inline9 which satisfy tex2html_wrap_inline11 in tex2html_wrap_inline13. This is the simplest example in the theory of compensated compactness for which the constant rank condition fails. The proof uses the fact that certain coefficients in the Haar basis expansion can be estimated in terms of the Riesz transform which seems to be of independent interest. Applications to the relation between rank-1 convexity and quasiconvexity are indicated.

24.11.2021, 02:10