The best constant of Sobolev inequality in an $n$ dimensional Euclidean space

The best constant of Sobolev inequality in an $n$ dimensional Euclidean space

Yoshinori Kametaka, Atsushi Nagai, and Kohtaro Watanabe

Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 81, Number 3 (2005), 57-60.

Abstract

The best constant of Sobolev inequality in an $n$ dimensional Euclidean space is found by means of the theory of reproducing kernel and Green function. The concrete form of the best constant is also found in the case of Sobolev space $W^2(\mathbf{R}^n)$ ($n=2,3$).

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Primary Subjects: 46E35, 46E22

Keywords: Best constant; Sobolev inequality; reproducing kernel; Green function

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1116442038
Mathematical Reviews number (MathSciNet): MR2128933
Digital Object Identifier: doi:10.3792/pjaa.81.57

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References

H. Brezis, Analyse fonctionnelle, Masson, Paris, 1983.

Mathematical Reviews (MathSciNet): MR697382

Zentralblatt MATH: 0511.46001

Y. Kametaka, K. Watanabe, A. Nagai and S. Pyatkov, The best constant of sobolev inequality in an $n$ dimensional eucledean space, Sci. Math. Jpn. 61 (2005), no.1, 15--23.

Mathematical Reviews (MathSciNet): MR2111539

C. Morosi and L. Pizzocchero, On the constants for some Sobolev imbeddings, J. Inequal. Appl. 6 (2001), no. 6, 665--679.

Mathematical Reviews (MathSciNet): MR1888258

K. Watanabe, T. Yamada and W. Takahashi, Reproducing kernels of $H\sp m(a,b)$ $(m=1,2,3)$ and least constants in Sobolev's inequalities, Appl. Anal. 82 (2003), no. 8, 809--820.

Mathematical Reviews (MathSciNet): MR2004289

Digital Object Identifier: doi:10.1080/0003681031000152541

Zentralblatt MATH: 1051.46021

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