A sharp integral inequality is proved and used to obtain a Sobolev interpolation inequality. Further, a new proof of a Gross-Sobolev logarithmic inequality is constructed on the basis of the Sobolev interpolation inequality.

中文翻译：

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Sobolev 插值不等式和 Gross-Sobolev 对数不等式

证明了一个尖锐的积分不等式并用于获得Sobolev插值不等式。此外，在 Sobolev 插值不等式的基础上构造了 Gross-Sobolev 对数不等式的新证明。