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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 Hessian equation ： ウィキペディア英語版 Hessian equation In mathematics, ''k''-Hessian equations (or Hessian equations for short) are partial differential equations (PDEs) based on the Hessian matrix. More specifically, a Hessian equation is the ''k''-trace, or the ''k''th elementary symmetric polynomial of eigenvalues of the Hessian matrix. When ''k'' ≥ 2, the ''k''-Hessian equation is a fully nonlinear partial differential equation.〔.〕 Much like differential equations often study the actions of differential operators (e.g. elliptic operators and elliptic equations), Hessian equations can be understood as simply eigenvalue equations acted upon by the Hessian differential operator. Special cases include the Monge–Ampère equation〔.〕 and Poisson's equation (the Laplacian being the trace of the Hessian matrix). These equations are of interest in geometric PDEs (a subfield at the interface between both geometric analysis and PDEs) and differential geometry. == References == 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「Hessian equation」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.