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Evaluation of the One-Dimensional L p Sobolev Type Inequality

Author

Listed:
  • Kazuo Takemura

    (General Education College of Science and Technology, Nihon University, Funabashi 274-0812, Japan
    Current address: 7-24-1, Narashinodai, Funabashi, Chiba 274-8501, Japan.
    These authors contributed equally to this work.)

  • Yoshinori Kametaka

    (Faculty of Engineering Science, Osaka University, Toyonaka 560-8531, Japan
    These authors contributed equally to this work.)

Abstract

This study applies the extended L 2 Sobolev type inequality to the L p Sobolev type inequality using Hölder’s inequality. The sharp constant and best function of the L p Sobolev type inequality are found using a Green function for the n th order ordinary differential equation. The sharp constant is shown to be equal to the L p norm of the Green function and to the p th root of the value of the origin of the best function.

Suggested Citation

  • Kazuo Takemura & Yoshinori Kametaka, 2020. "Evaluation of the One-Dimensional L p Sobolev Type Inequality," Mathematics, MDPI, vol. 8(2), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:296-:d:323568
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