Rank-one convexity implies quasiconvexity on diagonal matrices

Stefan Müller

Contact the author: Please use for correspondence this email.
Submission date: 02. May. 1999
Pages: 12
published in: International mathematics research notices, 1999 (1999) 20, p. 1087-1095 
Bibtex
MSC-Numbers: 49J45, 42C15, 35B35
Keywords and phrases: compensated compactness, quasiconvexity, wavelets, haar basis, riesz transform
Download full preprint: PDF (277 kB), PS ziped (138 kB)

Abstract:
We prove a conjecture of Tartar regarding weak lower semicontinuity of functionals on sequences which satisfy in . 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.