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 $W^2(\mathbf{R}^n)$ ($n=2,3$).
Citation
Yoshinori Kametaka. Atsushi Nagai. Kohtaro Watanabe. "The best constant of Sobolev inequality in an $n$ dimensional Euclidean space." Proc. Japan Acad. Ser. A Math. Sci. 81 (3) 57 - 60, March 2005. https://doi.org/10.3792/pjaa.81.57
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