Embeddings for the space $LD_\gamma^{p}$ on sets of finite perimeter
Abstract
Given an open set with finite perimeter $\Omega\subset \mathbb{R}^n$, we consider the space $LD_\gamma^{p}(\Omega)$, $1\leq p<\infty$, of functions with $p$th-integrable deformation tensor on $\Omega$ and with $p$ th-integrable trace value on the essential boundary of $\Omega$. 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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2018
- DOI:
- 10.48550/arXiv.1808.00611
- arXiv:
- arXiv:1808.00611
- Bibcode:
- 2018arXiv180800611C
- Keywords:
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- Mathematics - Analysis of PDEs;
- 46E35 (Primary);
- 74F10 (Secondary)
- E-Print:
- 20 pages, 3 figures