| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 30 | |
| Number of page(s) | 34 | |
| DOI | https://doi.org/10.1051/cocv/2019014 | |
| Published online | 24 March 2020 | |
On the continuity of the trace operator in GSBV (Ω) and GSBD (Ω)
SISSA,
via Bonomea 265,
34136
Trieste, Italy.
* Corresponding author: etasso@sissa.it
Received:
7
September
2018
Accepted:
17
March
2019
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.
Mathematics Subject Classification: 46E35 / 49Q20 / 26A45 / 26B30
Key words: Trace continuity / boundary conditions / free discontinuity problems / generalised bounded deformation / generalised bounded variation / jump set / rectifiable
© EDP Sciences, SMAI 2020
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