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Sharp Higher Order Adams’ Inequality with Exact Growth Condition on Weighted Sobolev Spaces

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Abstract

This paper introduces a novel higher order Adams inequality that incorporates an exact growth condition for a class of weighted Sobolev spaces. Our rigorous proof confirms the validity of this inequality and provides insights into the optimal nature of the critical constant and the exponent within the denominator. Furthermore, we apply this inequality to study a class of ordinary differential equations (ODEs), where we successfully derive both a concept of the weak solution and a comprehensive regularity theory.

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Acknowledgements

The authors would like to thank the referee for his/her careful reading and constructive comments.

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Authors and Affiliations

  1. Department of Mathematics, Federal University of Paraíba, João Pessoa, PB, 58051-900, Brazil

    João Marcos do Ó & Raoní Ponciano

  2. Department of Mathematics, University of Connecticut, Storrs, CT, 06269, USA

    Guozhen Lu

Authors
  1. João Marcos do Ó
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  2. Guozhen Lu
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  3. Raoní Ponciano
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Correspondence to Guozhen Lu.

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J. M. do Ò acknowledges partial support from CNPq through grants 312340/2021-4, 409764/2023-0, 443594/2023-6, CAPES MATH AMSUD grant 88887.878894/2023-00 and Paraíba State Research Foundation (FAPESQ), grant no 3034/2021, G. Lu acknowledges partial support from Simons collaboration through grants 519099 and 957892 and Simons Fellowship from Simons foundation, and R. Ponciano acknowledges partial support from CAPES through grants Nos. 88887.633572/2021-00 and 88881.689999/2022-01.

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do Ó, J.M., Lu, G. & Ponciano, R. Sharp Higher Order Adams’ Inequality with Exact Growth Condition on Weighted Sobolev Spaces. J Geom Anal 34, 139 (2024). https://doi.org/10.1007/s12220-024-01587-9

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