Evaluation of the One-Dimensional L p Sobolev Type Inequality

Kazuo Takemura and Yoshinori Kametaka
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Kazuo Takemura: General Education College of Science and Technology, Nihon University, Funabashi 274-0812, Japan
Yoshinori Kametaka: Faculty of Engineering Science, Osaka University, Toyonaka 560-8531, Japan

Mathematics, 2020, vol. 8, issue 2, 1-11

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.

Keywords: sobolev inequality; sharp constant; green function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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