1 results
Embeddings for the space
$LD_\gamma ^{p}$ on sets of finite perimeter
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 5 / October 2020
- Published online by Cambridge University Press:
- 07 May 2019, pp. 2442-2461
- Print publication:
- October 2020
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- Article
- Export citation
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Given an open set with finite perimeter
$\Omega \subset {\open R}^n$, we consider the space 
$LD_\gamma ^{p}(\Omega )$, 
$1\les p<\infty $, 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 
$LD_\gamma ^{p}(\Omega )\subset L^{pN/(N-1)}(\Omega )$. The space 
$LD_\gamma ^{p}(\Omega )$ and this embedding arise naturally in studying the motion of rigid bodies in a viscous, incompressible fluid.
