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Equivalence of solutions of eikonal equation in metric spaces
https://oist.repo.nii.ac.jp/records/1901
https://oist.repo.nii.ac.jp/records/190191528ba6-3ee9-4f5b-9f43-88af1bc85a89
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
HJ_metric_final (554.1 kB)
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International(https://creativecommons.org/licenses/by-nc-nd/4.0/)
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| Item type | 学術雑誌論文 / Journal Article(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2021-01-20 | |||||
| タイトル | ||||||
| タイトル | Equivalence of solutions of eikonal equation in metric spaces | |||||
| 言語 | en | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| キーワード | ||||||
| 言語 | en | |||||
| 主題Scheme | Other | |||||
| 主題 | Eikonal equation | |||||
| キーワード | ||||||
| 言語 | en | |||||
| 主題Scheme | Other | |||||
| 主題 | Viscosity solutions | |||||
| キーワード | ||||||
| 言語 | en | |||||
| 主題Scheme | Other | |||||
| 主題 | Metric spaces | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
| 資源タイプ | journal article | |||||
| 著者（英） |
Liu, Qing
× Liu, Qing× Shanmugalingam, Nageswari× Zhou, Xiaodan |
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| 書誌情報 |
en : Journal of Differential Equations 巻 272, p. 979-1014, 発行日 2020-10-21 |
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| 抄録 | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | In this paper we prove the equivalence between some known notions of solutions to the eikonal equation and more general analogs of the Hamilton-Jacobi equations in complete and rectifiably connected metric spaces. The notions considered are that of curve-based viscosity solutions, slope-based viscosity solutions, and Monge solutions. By using the induced intrinsic (path) metric, we reduce the metric space to a length space and show the equivalence of these solutions to the associated Dirichlet boundary problem. Without utilizing the boundary data, we also localize our argument and directly prove the equivalence for the definitions of solutions. Regularity of solutions related to the Euclidean semi-concavity is discussed as well. | |||||
| 出版者 | ||||||
| 出版者 | Elsevier | |||||
| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 0022-0396 | |||||
| DOI | ||||||
| 関連タイプ | isVersionOf | |||||
| 識別子タイプ | DOI | |||||
| 関連識別子 | info:doi/10.1016/j.jde.2020.10.018 | |||||
| 権利 | ||||||
| 権利情報 | This article/chapter was published in Journal of Differential Equations, Volume 272, Qing Liu, Nageswari Shanmugalingam, Xiaodan Zhou, Equivalence of solutions of eikonal equation in metric spaces, Page 979-1014, © Elsevier 2020. | |||||
| 関連サイト | ||||||
| 識別子タイプ | URI | |||||
| 関連識別子 | https://www.sciencedirect.com/science/article/pii/S002203962030560X | |||||
| 著者版フラグ | ||||||
| 出版タイプ | AM | |||||
| 出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||
