| 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 |
| . |
