Upper bound of the best constant of a trudinger-moser inequality and its application to A Gagliardo-Nirenberg inequality

Hideo Kozono; Tokushi Sato; Hidemitsu Wadade

doi:10.1512/iumj.2006.55.2743

Upper bound of the best constant of a trudinger-moser inequality and its application to A Gagliardo-Nirenberg inequality

Hideo Kozono, Tokushi Sato, Hidemitsu Wadade

数理科学連携研究センター

研究成果: Article › 査読

63 被引用数 (Scopus)

抄録

We will consider a Trudinger-Moser inequality for the critical Sobolev space H^n/p,p(ℝⁿ) with the fractional derivatives in ℝⁿ and obtain an upper bound of the best constant of such an inequality. Moreover, by changing normalization from the homogeneous norm to the inhomogeneous one, we will give the best constant in the Hubert space H ^n/2,2(ℝⁿ). As an application, we will obtain some lower bound of the best constant of a Gagliardo-Nirenberg inequality. Indiana University Mathematics Journal

本文言語	English
ページ（範囲）	1951-1974
ページ数	24
ジャーナル	Indiana University Mathematics Journal
巻	55
号	6
DOI	https://doi.org/10.1512/iumj.2006.55.2743
出版ステータス	Published - 2006 12月 1

ASJC Scopus subject areas

数学 (全般)

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10.1512/iumj.2006.55.2743

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KW - Average function

KW - Fractional integral

KW - Gagliadro-Nirenberg inequality

KW - Rearrangement

KW - Riesz potential

KW - Sobolev inequality

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Upper bound of the best constant of a trudinger-moser inequality and its application to A Gagliardo-Nirenberg inequality

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