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A note on the second order geometric Rellich inequality on half-space

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Abstract

We prove a two-parameter family of second order geometric Rellich type equalities on the half-space \( \mathbb {R} _{+}^{n}\). We then use it to derive several refined geometric Rellich type inequalities. We also prove an improved version of the Rellich–Sobolev–Maz’ya type inequality.

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Acknowledgements

The authors would like to thank Professor Fritz Gesztesy for his valuable comments. They also wish to thank the anonymous referee for many useful suggestions on the earlier version which have helped its exposition of the paper.

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Authors and Affiliations

  1. Faculty of Economics and Law, University of Finance-Marketing, 778 Nguyen Kiem St., District Phu Nhuan, HCM City, Vietnam

    Nguyen Tuan Duy

  2. School of Science and the Environment, Grenfell Campus, Memorial University of Newfoundland, Corner Brook, NL, A2H5G4, Canada

    Nguyen Lam

  3. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Le Long Phi

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  1. Nguyen Tuan Duy
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  2. Nguyen Lam
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Correspondence to Le Long Phi.

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Communicated by Gerald Teschl.

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Duy, N.T., Lam, N. & Phi, L.L. A note on the second order geometric Rellich inequality on half-space. Monatsh Math 195, 233–248 (2021). https://doi.org/10.1007/s00605-020-01490-9

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