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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Strichartz estimate ： ウィキペディア英語版 Strichartz estimate In applied mathematics, Strichartz estimates are a family of inequalities for linear dispersive partial differential equations. These inequalities establish size and decay of solutions in mixed norm Lebesgue spaces. They were first noted by R. Strichartz and arose out of contentions to the Fourier restriction problem. == Examples == Consider the linear Schrödinger equation in $\backslash mathbb^d$ with ''h'' = ''m'' = 1. Then the solution for initial data $u\_0$ is given by $e^u\_0$. Let ''q'' and ''r'' be real numbers satisfying $2\backslash leq\; q,\; r\; \backslash leq\; \backslash infty$; $\backslash frac+\backslash frac=\backslash frac$; and $(q,r,d)\backslash neq(2,\backslash infty,2)$. In this case the homogeneous Strichartz estimates take the form: :$\backslash |e^\; u\_0\backslash |\_\backslash leq\; C\_\; \backslash |u\_0\backslash |\_2.$ Further suppose that $\backslash tilde\; q,\; \backslash tilde\; r$ satisfy the same restrictions as $q,\; r$ and $\backslash tilde\; q\text{'},\; \backslash tilde\; r\text{'}$ are their dual exponents, then the dual homogeneous Strichartz estimates take the form:〔 :$\backslash left\backslash |\; \backslash int\_\backslash mathbb\; e^F(s)\backslash ,ds\backslash right\backslash |\_\backslash leq\; C\_\backslash |F\backslash |\_\_x\}.$ The inhomogeneous Strichartz estimates are:〔 :$\backslash left\backslash |\; \backslash int\_\; e^F(s)\backslash ,ds\backslash right\backslash |\_\backslash leq\; C\_\backslash |F\backslash |\_\_x\}.$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Strichartz estimate」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.