Differential Equations and Numerical Analysis Seminar - 26/10/2011

Wednesday, 26 October 2011, 12:00 p.m.

Lecturer: Carolin Kreisbeck, CMA, FFCT/UNL

Title: "Thin-film limits of functionals on A-free vector fields and applications”.

Local: Room 1.5, Edifício VII
Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

 

Abstract: Working with variational principles that are subject to linear PDE constraints conveyed by a constant-rank operator A allows to treat a wide range of problems in continuum mechanics and electromagnetism in a unified way. In this contribution, 3d-2d dimension reduction is studied within the A-free framework. We investigate, by means of Gamma-convergence, the effective behavior of integral functionals as the thickness of the domain tends to zero. The limit functional turns out to be determined by the A-quasiconvex envelope and is constrained to vector fields that satisfy limit PDEs, which are in general different from the ones we started with. As applications, we give the full characterization of a thin-film Gamma-limit in micromagnetics and answer an, up to now, open question regarding locality of the energy of a membrane model in nonlinear elasticity.