The best constant of Sobolev inequality in an $n$ dimensional Euclidean space
Kametaka, Yoshinori ; Watanabe, Kohtaro ; Nagai, Atsushi
Proc. Japan Acad. Ser. A Math. Sci., Tome 81 (2005) no. 3, p. 57-60 / Harvested from Project Euclid
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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 $W^2(\mathbf{R}^n)$ ($n=2,3$).
Publié le : 2005-03-14
Classification:  Best constant,  Sobolev inequality,  reproducing kernel,  Green function,  46E35,  46E22 
@article{1116442038,
     author = {Kametaka, Yoshinori and Watanabe, Kohtaro and Nagai, Atsushi},
     title = {The best constant of Sobolev inequality in an $n$ dimensional
 Euclidean space},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {81},
     number = {3},
     year = {2005},
     pages = { 57-60},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1116442038}
}

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., Tome 81 (2005) no. 3, pp.  57-60. http://gdmltest.u-ga.fr/item/1116442038/