Volume 7, 2002
|Page(s)||309 - 334|
|Published online||15 September 2002|
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.