Article

 Title: A remark on polyconvex envelopes of radially symmetric functions in dimension $2\times 2$ (English) Author: Došlý, Ondřej Language: English Journal: Applications of Mathematics ISSN: 0862-7940 (print) ISSN: 1572-9109 (online) Volume: 42 Issue: 3 Year: 1997 Pages: 195-212 Summary lang: English . Category: math . Summary: We study polyconvex envelopes of a class of functions related to the function of Kohn and Strang introduced in . We present an example of a function of this class for which the polyconvex envelope may be computed explicitly and we also point out some general features of the problem. (English) Keyword: polyconvex envelope Keyword: rank one convex envelope Keyword: lower semicontinuous functional Keyword: quasiconvex functional Keyword: coercive integral functional Keyword: radially symmetric function of Kohn-Strang type MSC: 49J40 MSC: 49J45 MSC: 73C50 MSC: 73V25 MSC: 90C26 idZBL: Zbl 0904.49012 idMR: MR1441630 DOI: 10.1023/A:1022417621327 . Date available: 2009-09-22T17:54:29Z Last updated: 2020-07-02 Stable URL: http://hdl.handle.net/10338.dmlcz/134353 . Reference: [1] J. M. Ball: Convexity and existence theorems in nonlinear elasticity.Arch. Rational Mech. Anal. 63 (1977), 337–403. MR 0475169, 10.1007/BF00279992 Reference: [2] B. Dacarogna: Direct Methods in the Calculus of Variations.Springer-Verlag, New-York 1989. MR 0990890 Reference: [3] B. Dacarogna, H. Koshigoe: On the different notions of convexity for rationally invariant functions.preprint. Reference: [4] R. Kohn, G. Strang: Optimal design and relaxation of variational problems I, II and III.Comm. Pure Appl. Math. 39 (1986), 113–137, 139–182, 353–377. MR 0820342, 10.1002/cpa.3160390305 Reference: [5] C. B. Morrey: Quasiconvexity and the semicontinuity of multiple integrals.Pacific. J. Math. 2 (1952), 25–53. MR 0054865, 10.2140/pjm.1952.2.25 .

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