×

Rank-one connections at infinity and quasiconvex hulls. (English) Zbl 0976.49009

The author’s own definition of \(p\)-quasiconvex hull \(Q_p(K)\) of a set \(K\subset \mathbb{R}^{N\times n}\) of matrices, i.e., the zero-set of a standard quasiconvex hull of the \(p\)-power of the Euclidean distance from \(K\), is used. Focusing on \(K\) unbounded, \(K\) is said to have a \(p\)-rank-one connection at infinity if, for some sequence \(\{A_j\}\subset K\), the greatest eigenvalue of \(A^T_jA_j\) goes to infinity faster than all other eigenvalues. It is shown that \(Q_p(K)\) may be bigger than \(K\) if \(K\) has a \(p\)-rank-one condition. Some examples are examined and a comparison with another, more restrictive B.-S. Yan’s definition of a quasiconvex hull is made.

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
74N15 Analysis of microstructure in solids
PDFBibTeX XMLCite
Full Text: EuDML EMIS