A study on vector valued functions spaces based on T-convergence

Abstract

The object of 􀀀-convergence is the description of the asymptotic behaviour of families of minimum problems, usually depending on some parameters whose nature may be geometric or constitutive, deriving from a discretization argument, an approximation procedure, etc. Since its introduction by DE Giorgi in the early 1970s 􀀀-convergence has gained an undiscussed role as the most exible and natural notation of convergence for variational problems and is now widely used also outside the the eld os calculas of variation and partial diferential equations. In this way 􀀀-convergence is not bound to any prescribed setting, and it can be applied to the study of problems with discontinuities in computer vision as well as to description of the overall properties of non linear composites, to the formalization of the passage from discrete systems to continuum theories, to the modeling of thin lms or plates, etc., and may be potentially of help in a great variety of situations where a variational limit intervenes or an approximation process is needed. In this thesis we study the asymptotic behavior of the sequence of nonlinear functionals, including some hyperelastic energies , de ned on vector-valued functions by 􀀀-convergence as follows;