caa a22 4500 388109041 CHVBK 20180307125348.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500021454 doi S0308210500021454 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500021454 Minimizers for a double-well problem with affine boundary conditions [Elektronische Daten] This paper is concerned with the existence of minimizers for functionals having a double-well integrand with affine boundary conditions. Such functionals are related to the so-called Kohn-Strang functional, which arises in optimal shape design problems in electrostatics or elasticity. They are known to be not quasiconvex, and therefore existence of minimizers is, in general, guaranteed only for their quasiconvex envelopes. We generalize the previous results of Allaire and Francfort, and give necessary and sufficient conditions on the affine boundary conditions for existence of minimizers. Our method relies on the computation of the quasiconvexification of these functionals by using homogenization theory. We also prove by a general argument that their rank-one convexifications coincide with their quasiconvexifications. Copyright © Royal Society of Edinburgh 1999 Allaire Grégoire Laboratoire d'Analyse Numérique, Université Paris 6, 75252 Paris Cedex 05, France Lods Véronique Laboratoire d'Analyse Numérique, Université Paris 6, 75252 Paris Cedex 05, France Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/3(1999), 439-466 0308-2105 129:3<439 1999 129 PRM https://doi.org/10.1017/S0308210500021454 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500021454 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Allaire Grégoire Laboratoire d'Analyse Numérique, Université Paris 6, 75252 Paris Cedex 05, France NATIONALLICENCE 700 1- Lods Véronique Laboratoire d'Analyse Numérique, Université Paris 6, 75252 Paris Cedex 05, France NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/3(1999), 439-466 0308-2105 129:3<439 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge