Sharp numerical inclusion of the best constant for embedding on bounded convex domain

Sharp numerical inclusion of the best constant for embedding on bounded convex domain

In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding on a bounded convex domain in . We estimate the best constant by computing the corresponding extremal function using a verified numerical computation. Verified numerical inclu...

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Veröffentlicht in:Journal of computational and applied mathematics 2017-02, Vol.311, p.306-313
Hauptverfasser: Tanaka, Kazuaki, Sekine, Kouta, Mizuguchi, Makoto, Oishi, Shin'ichi
Format: Artikel
Sprache:eng
Schlagworte:
Computation
Constants
Estimates
Inclusions
Mathematical analysis
Mathematical models
Numerical analysis
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Zusammenfassung:In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding on a bounded convex domain in . We estimate the best constant by computing the corresponding extremal function using a verified numerical computation. Verified numerical inclusions of the best constant on a square domain are presented.
ISSN:0377-0427
DOI:10.1016/j.cam.2016.07.021