An explicit formula of reduced membrane energy for incompressible p-Dirichlet energy

Abstract

In this article, a model problem on thin-film limit of p-Dirichlet energy for incompressible deformations is studied. An explicit formula is given for the relaxation of special nonconvex functional

for mappings u from a bounded domain Ω ⊂ R ² to R ³. The formula provides the explicit reduced membrane energy from the p-Dirichlet energy for incompressible elastic materials.

Keywords:

• membrane energy
• incompressible p-Dirichlet energy
• quasiconvexification

AMS Subject Classifications:

• 49J45
• 74B20
• 74G65