Quasiconvexification of sets in optimal design
2009 - O. Boussaid, P. Pedregal
Calculus of Variations and Partial Differential Equations 34, 139-152 (2009)
Pedregal Tercero, Pablo.
By a suitable reformulation of a typical optimal design problem in conductivity, we treat the issue of determining the quasiconvexification (to fixed volume fraction) of certain sets of matrices that are union of two manifolds. By means of a helpful lemma, we are able to explicitly compute such hulls in a rather straightforward fashion without the need of seeking laminates by hand, and hence avoiding some tedious computations. We examine the linear case, both elliptic and hyperbolic, in 2 and higher dimension (by looking at a div-curl situation), as well as an interesting non-linear example that provides some clue as to what kind of characterization one may hope for in non-linear situations.