Numerical Computation of Rank-One Convex Envelopes

Abstract

Previous article Next article Numerical Computation of Rank-One Convex EnvelopesGeorg DolzmannGeorg Dolzmannhttps://doi.org/10.1137/S0036142997325581PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractWe describe an algorithm for the numerical computation of the rank-one convex envelope of a function $f:\MM^{m\times n}\rightarrow\RR$. We prove its convergence and an error estimate in $L^\infty$.[1] Robert Aumann and , Sergiu Hart, Bi‐convexity and bi‐martingales, Israel J. Math., 54 (1986), 159–180 87k:90304 CrossrefISIGoogle Scholar[2] J. M. Ball and and R. D. James, Proposed experimental tests of a theory of fine microstructure and the two‐well problem, Philos. Trans. Roy. Soc. London Ser. A, 338 (1992), pp. 389–450. ptr PTRMAD 0962-8428 Philos. Trans. R. Soc. London, Ser. A CrossrefISIGoogle Scholar[3] Kaushik Bhattacharya, , Nikan Firoozye, , Richard James and , Robert Kohn, Restrictions on microstructure, Proc. Roy. Soc. Edinburgh Sect. 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