CMU Campus
Center for                           Nonlinear Analysis
CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact
Publication 10-CNA-18

Characterization of the Multiscale Limit Associated with Bounded Sequences in BV

Rita Ferreira
I.C.T.I. - Carnegie Mellon | Portugal, F.C.T./C.M.A. da U.N.L.
Quinta da Torre
2829.516 Caparica, Portugal
rferreir@andrew.cmu.edu, ragf@fct.unl.pt

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213, USA
fonseca@andrew.cmu.edu

Abstract:The notion of two-scale convergence for sequences of Radon measures with finite total variation is generalized to the case of multiple periodic length scales of oscillations. The main result concerns the characterization of $ (n+1)$-scale limit pairs $ (u,U)$ of sequences $ \{(u_\varepsilon{\mathcal{L}^N\!}_{\lfloor\Omega}, {Du_\varepsilon}_{\lfloor\O... ...cal{ M}(\Omega;\mathbb{R}^d)\times \mathcal{ M}(\Omega;\mathbb{R}^{d\times N})$ whenever $ \{u_\varepsilon\}_{\varepsilon>0}$ is a bounded sequence in $ BV(\Omega;\mathbb{R}^d)$. This characterization is useful in the study of the asymptotic behavior of periodically oscillating functionals with linear growth, defined on the space $ BV$ of functions of bounded variation and described by $ n\in\mathbb{N}$ microscales, undertaken in [10].

([10] R. Ferreira, I. Fonseca, Reiterated Homogenization in $ BV$ via Multiscale Convergence, in preparation)

Get the paper in its entirety as

Back to CNA Publications