Relaxation of Quasilinear Elliptic Systems via A-quasiconvex Envelopes
Institute of Mathematics and Computer Science,
University of Latvia, 1459 Riga, Latvia;
Received: November 2001
We consider the weak closure WZ of the set Z of all feasible pairs (solution, flow) of the family of potential elliptic systems where Ω ⊂ Rn is a bounded Lipschitz domain, Fs are strictly convex smooth functions with quadratic growth and . We show that WZ is the zero level set for an integral functional with the integrand being the A-quasiconvex envelope for a certain function and the operator A = (curl,div)m. If the functions Fs are isotropic, then on the characteristic cone Λ (defined by the operator A) coincides with the A-polyconvex envelope of and can be computed by means of rank-one laminates.
Mathematics Subject Classification: 49J45
Key words: Quasilinear elliptic system / relaxation / A-quasiconvex envelope.
© EDP Sciences, SMAI, 2002