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The purpose of this article is twofold. The first aim is to prove that ifthere exist a sequence $\{\varphi_j\}\subset \mathrm{Aut}(\Omega)$ and $a\in\Omega$ such that $\lim_{j\to\infty}\varphi_j(a)=\xi_0$ and$\lim_{j\to\infty}\sigma_\Omega(\varphi_j(a))=1$, where $\xi_0$ is a linearlyconvex boundary point of finite type, then $\xi_0$ must be stronglypseudoconvex. Then, the second aim is to investigate the boundary behaviour ofthe squeezing function of a general ellipsoid.

On the boundary behaviour of the squeezing function near linearly convex boundary points