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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 Semi-elliptic operator ： ウィキペディア英語版 Semi-elliptic operator In mathematics — specifically, in the theory of partial differential equations — a semi-elliptic operator is a partial differential operator satisfying a positivity condition slightly weaker than that of being an elliptic operator. Every elliptic operator is also semi-elliptic, and semi-elliptic operators share many of the nice properties of elliptic operators: for example, much of the same existence and uniqueness theory is applicable, and semi-elliptic Dirichlet problems can be solved using the methods of stochastic analysis. ==Definition== A second-order partial differential operator ''P'' defined on an open subset Ω of ''n''-dimensional Euclidean space R''n'', acting on suitable functions ''f'' by :$P\; f(x)\; =\; \backslash sum\_^\; a\_\; (x)\; \backslash frac\}(x)\; +\; \backslash sum\_^\; b\_\; (x)\; \backslash frac\{\backslash partial\; x\_\{i\}\}\; (x)\; +\; c(x)\; f(x),$ is said to be semi-elliptic if all the eigenvalues ''λ''''i''(''x''), 1 ≤ ''i'' ≤ ''n'', of the matrix ''a''(''x'') = (''a''''ij''(''x'')) are non-negative. (By way of contrast, ''P'' is said to be elliptic if ''λ''''i''(''x'') > 0 for all ''x'' ∈ Ω and 1 ≤ ''i'' ≤ ''n'', and uniformly elliptic if the eigenvalues are uniformly bounded away from zero, uniformly in ''i'' and ''x''.) Equivalently, ''P'' is semi-elliptic if the matrix ''a''(''x'') is positive semi-definite for each ''x'' ∈ Ω. 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「Semi-elliptic operator」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.