We prove that the displacement problem of inhomogeneous elastostatics in a two--dimensional exterior Lipschitz domain has a unique solution with finite Dirichlet integral $\u$, vanishing uniformly at infinity if and only if the boundary datum satisfies a suitable compatibility condition (Stokes' paradox). Moreover, we prove that it is unique under the sharp condition $\u=o(\log r)$ and decays uniformly at infinity with a rate depending on the elasticities. In particular, if these last ones tend to a homogeneous state at large distance, then $\u=O(r^{-\alpha})$, for every $\alpha<1$.

中文翻译：

---

非均匀弹性静力学中的斯托克斯悖论

我们证明了二维外部 Lipschitz 域中非均匀弹性静力学的位移问题具有唯一解，其中有限 Dirichlet 积分 $\u$，当且仅当边界基准满足合适的相容性条件（Stokes'悖论）。此外，我们证明了它在尖锐条件 $\u=o(\log r)$ 下是唯一的，并且在无穷远时以取决于弹性的速率均匀衰减。特别是，如果最后这些在远距离趋于同质状态，则 $\u=O(r^{-\alpha})$，对于每一个 $\alpha<1$。