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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

63 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	1951-1974
Number of pages	24
Journal	Indiana University Mathematics Journal
Volume	55
Issue number	6
DOIs	https://doi.org/10.1512/iumj.2006.55.2743
Publication status	Published - 2006 Dec 1
Externally published	Yes

Keywords

Average function
Fractional integral
Gagliadro-Nirenberg inequality
Rearrangement
Riesz potential
Sobolev inequality
Trudinger-Moser inequality

ASJC Scopus subject areas

Mathematics(all)

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10.1512/iumj.2006.55.2743

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abstract = "We will consider a Trudinger-Moser inequality for the critical Sobolev space Hn/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",

keywords = "Average function, Fractional integral, Gagliadro-Nirenberg inequality, Rearrangement, Riesz potential, Sobolev inequality, Trudinger-Moser inequality",

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AU - Sato, Tokushi

AU - Wadade, Hidemitsu

PY - 2006/12/1

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N2 - We will consider a Trudinger-Moser inequality for the critical Sobolev space Hn/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

AB - We will consider a Trudinger-Moser inequality for the critical Sobolev space Hn/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

KW - Average function

KW - Fractional integral

KW - Gagliadro-Nirenberg inequality

KW - Rearrangement

KW - Riesz potential

KW - Sobolev inequality

KW - Trudinger-Moser inequality

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

Abstract

Keywords

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