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Some Inequalities for Partial Derivatives on Time Scales

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Abstract

We prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial differential dynamic equations are also considered.

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Acknowledgments

The author would like to express his deepest gratitude to Assoc. Prof. Dinh Thanh Duc, Prof. Vu Kim Tuan and Nguyen Du Vi Nhan for their comments and suggestions to improve this paper.

This work is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2014.32.

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Authors and Affiliations

  1. Department of Mathematics, Quy Nhon University, Binh Dinh, Vietnam

    Tran Dinh Phung

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  1. Tran Dinh Phung
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Correspondence to Tran Dinh Phung.

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Phung, T.D. Some Inequalities for Partial Derivatives on Time Scales. Acta Math Vietnam 42, 369–394 (2017). https://doi.org/10.1007/s40306-016-0187-7

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  • DOI: https://doi.org/10.1007/s40306-016-0187-7

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