Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

Yoshinori Kametaka, Atsushi Nagai, and Kohtaro Watanabe

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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 $W^2(\mathbf{R}^n)$ ($n=2,3$).

Article information

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

Dates
First available in Project Euclid: 18 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1116442038

Digital Object Identifier
doi:10.3792/pjaa.81.57

Mathematical Reviews number (MathSciNet)
MR2128933

Zentralblatt MATH identifier
1100.46021

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 46E22: Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]

Keywords
Best constant Sobolev inequality reproducing kernel Green function

Citation

Kametaka, Yoshinori; Watanabe, Kohtaro; Nagai, Atsushi. The best constant of Sobolev inequality in an $n$ dimensional Euclidean space. Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 3, 57--60. doi:10.3792/pjaa.81.57. https://projecteuclid.org/euclid.pja/1116442038


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References

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