We prove the non-degeneracy of the extremals of the Sobolev inequality \[ \int_{\mathbb R^N}|\nabla u|^p\,\rd x\ge \mathcal S_p\int_{\open R^N}|u|^\frac{Np}{N-p}\,\rd x,\quad u\in \mathcal D^{1,p}(\open R^N) \] when 1 < p < N, as solutions of a critical quasilinear equation involving the p-Laplacian.

中文翻译：

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临界 p-Laplace 方程泡的非退化性

我们证明了 Sobolev 不等式的极值的非退化性\[ \int_{\mathbb R^N}|\nabla u|^p\,\rd x\ge \mathcal S_p\int_{\open R^N}|u|^\frac{Np}{Np}\ ,\rd x,\quad u\in \mathcal D^{1,p}(\open R^N) \]当 1 <p<ñ，作为一个关键拟线性方程的解，涉及p-拉普拉斯算子。