RELAXATION OF FUNCTIONALS INVOLVING HOMOGENEOUS FUNCTIONS AND INVARIANCE OF ENVELOPES

The authors compute the quasiconvex envelope of certain functions defined on the space M,.mn of real m x n matrices via a homogeneous function on Mmn - They also deduce Invariance properties for various convex envelopes from corresponding invariance properties satisfied by a function. Some applications related in particular to nonlinear elasticity arc given.

On Nonlinearly Elastic Membranes under Compression

古典方程一非，用 SaintVenant-Kirchhoff 材料做的线性地有弹性的飞机膜被福克斯， Raoult 和 Simo 和 Pantz (2000 )(1993 ) 认为正当。在压缩下面，联系最小化问题承认的 Weshow 没有答案。证明基于 minimizers 的不存在的结果非凸由于 Dacorogna andMarcellini (1995 ) 功能。我们从飞机弹性概括他们的结果的申请 tothree 维的飞机膜。