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 Γ, 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.
Keywords: Trace continuity, boundary conditions, free discontinuity problems, generalised bounded deformation, generalised bounded variation, jump set, rectifiable
@article{COCV_2020__26_1_A30_0,
author = {Tasso, Emanuele},
title = {On the continuity of the trace operator in {\protect\emph{GSBV}} {(\ensuremath{\Omega})} and {\protect\emph{GSBD}} {(\ensuremath{\Omega})}},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2020},
publisher = {EDP Sciences},
volume = {26},
doi = {10.1051/cocv/2019014},
mrnumber = {4079210},
zbl = {1453.46036},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2019014/}
}
TY - JOUR AU - Tasso, Emanuele TI - On the continuity of the trace operator in GSBV (Ω) and GSBD (Ω) JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2019014/ DO - 10.1051/cocv/2019014 LA - en ID - COCV_2020__26_1_A30_0 ER -
%0 Journal Article %A Tasso, Emanuele %T On the continuity of the trace operator in GSBV (Ω) and GSBD (Ω) %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2019014/ %R 10.1051/cocv/2019014 %G en %F COCV_2020__26_1_A30_0
Tasso, Emanuele. On the continuity of the trace operator in GSBV (Ω) and GSBD (Ω). ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 30. doi: 10.1051/cocv/2019014
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