@article{f4a532c746484ff68fd9dd9305b0fa02,
title = "Sharp numerical inclusion of the best constant for embedding H01(Ω)↪Lp(Ω) on bounded convex domain",
abstract = "In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding H01(Ω)↪Lp(Ω) on a bounded convex domain in R2. 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.",
keywords = "Computer-assisted proof, Elliptic problem, Embedding constant, Error bounds, Sobolev inequality, Verified numerical computation",
author = "Kazuaki Tanaka and Kouta Sekine and Makoto Mizuguchi and Shin'ichi Oishi",
note = "Funding Information: This work was supported by CREST, Japan Science and Technology Agency . The first author (K.T.) is supported by the Waseda Research Institute for Science and Engineering , the Grant-in-Aid for Young Scientists (Early Bird Program). The second author (K.S.) is supported by JSPS KAKENHI Grant Number 16K17651 . Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",
year = "2017",
month = feb,
day = "1",
doi = "10.1016/j.cam.2016.07.021",
language = "English",
volume = "311",
pages = "306--313",
journal = "Journal of Computational and Applied Mathematics",
issn = "0377-0427",
publisher = "Elsevier",
}