On the continuity of the trace operator in GSBV (Ω) and GSBD (Ω)
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Date
2018-09
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Abstract
In this paper we present a new result of continuity for the trace operator acting on
functions that might jump on a prescribed (n−1)-dimensional set Г, with the only hypothesis
of being rectifiable and of finite measure. We also show an application of our result in relation
to the variational model of elasticity with cracks, when the associated minimum problems are
coupled with Dirichlet and Neumann boundary conditions.
Description
27 pages
Keywords
trace continuity, boundary conditions, free discontinuity problems, generalised bounded deformation, generalised bounded variation, jump set, rectifiable