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Sharp Sobolev inequalities involving boundary terms revisited

Abstract

We revisit the sharp Sobolev inequalities involving boundary terms on Riemannian manifolds with boundaries proved by Li and Zhu (Geom Funct Anal 8: 59–87, 1998) and explore the role of the mean curvature.

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Acknowledgements

J. Xiong would like to thank Tianling Jin for valuable discussions.

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Correspondence to Zhongwei Tang.

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Communicated by N. Trudinger.

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Z. Tang is supported by NSFC (No. 12071036).

J. Xiong is partially supported by the National Key R&D Program of China (No. 2020YFA0712900) and NSFC (No. 11922104,11631002).

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Tang, Z., Xiong, J. & Zhou, N. Sharp Sobolev inequalities involving boundary terms revisited. Calc. Var. 60, 160 (2021). https://doi.org/10.1007/s00526-021-02036-z

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