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A natural approach to the asymptotic mean value property for the p-Laplacian
http://hdl.handle.net/2297/48570
http://hdl.handle.net/2297/4857093f38f8f-9f21-471a-95b8-b29f56a5b719
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
TE-PR-WATADE-H-97.pdf (159.0 kB)
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| アイテムタイプ | 学術雑誌論文 / Journal Article(1) | |||||
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| 公開日 | 2017-12-05 | |||||
| タイトル | ||||||
| タイトル | A natural approach to the asymptotic mean value property for the p-Laplacian | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 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 |
Ishiwata, Michinori
× Ishiwata, Michinori× Magnanini, Rolando× Wadade, Hidemitsu |
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| 書誌情報 |
Calculus of Variations and Partial Differential Equations 巻 56, 号 4, p. 97, 発行日 2017-08-01 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 0944-2669 | |||||
| NCID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA10848617 | |||||
| DOI | ||||||
| 関連タイプ | isVersionOf | |||||
| 識別子タイプ | DOI | |||||
| 関連識別子 | 10.1007/s00526-017-1188-7 | |||||
| 出版者 | ||||||
| 出版者 | Springer New York LLC | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | Let 1 ≤ p≤ ∞. We show that a function u∈ C(RN) is a viscosity solution to the normalized p-Laplace equation Δpnu(x)=0 if and only if the asymptotic formula (Formula Presented.) holds as ε→ 0 in the viscosity sense. Here, μp(ε, u) (x) is the p-mean value of u on Bε(x) characterized as a unique minimizer of (Formula Presented.) with respect to λ∈ R. This kind of asymptotic mean value property (AMVP) extends to the case p= 1 previous (AMVP)’s obtained when μp(ε, u) (x) is replaced by other kinds of mean values. The natural definition of μp(ε, u) (x) makes sure that this is a monotonic and continuous (in the appropriate topology) functional of u. These two properties help to establish a fairly general proof of (AMVP), that can also be extended to the (normalized) parabolic p-Laplace equation. © 2017, Springer-Verlag Berlin Heidelberg. | |||||
| 内容記述 | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | Embargo Period 12 months | |||||
| 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 | |||||
