Given an open set with finite perimeter, we consider the space, LDpγ(Ω), 1 ≤p < ∞, of functions with pth-integrable deformation tensor on Ω and with pth-integrable trace value on the essential boundary of Ω. We establish the continuous embedding. The space and this embedding arise naturally in studying the motion of rigid bodies in a viscous, incompressible fluid.
|Original language||English (US)|
|Number of pages||20|
|Journal||Proceedings of the Royal Society of Edinburgh Section A: Mathematics|
|State||Published - Oct 1 2020|
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