We consider weak positive solutions to the critical p-Laplace equation with Hardy potential in ${\mathbb{R}}^N$$-{\mathrm{\Delta }}_{p}u-\frac{\gamma }{|x{|}^p}{u}^{p-1}=u^{p^{⁎}-1}$ where $1<p<N$, $0⩽\gamma <{\left(\frac{N-p}{p}\right)}^p$ and $p^{⁎}=\frac{Np}{N-p}$.

The main result is to show that all the solutions in ${\mathcal{D}}^{1,p}({\mathbb{R}}^N)$ are radial and radially decreasing about the origin.

中文翻译：

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具有临界Sobolev增长和Hardy势的拟线性椭圆方程的径向对称

我们考虑了具有Hardy势的临界p -Laplace方程的弱正解${\mathbb{[R}}^{ñ}$$-{\mathrm{\Delta }}_pü-\frac{\gamma }{|X{|}^p}{ü}^{p-\mathrm{1个}}={ü}^{p^{⁎}-\mathrm{1个}}$ 哪里 $\mathrm{1个}<p<ñ$， $0⩽\gamma <{（\frac{ñ-p}{p}）}^p$ 和 $p^{⁎}=\frac{ñp}{ñ-p}$。

主要结果是表明 ${\mathcal{d}}^{\mathrm{1个}，p}（{\mathbb{[R}}^{ñ}）$ 沿原点呈径向和径向减小。