Nemytskii operator について

Words near each other

Dictionary Lists

mini英和辞書

mini和英辞書

翻訳と辞書　辞書検索 [ 開発暫定版 ]

スポンサードリンク

Nemytskii operator ：ウィキペディア英語版

Nemytskii operator
In mathematics, Nemytskii operators are a class of nonlinear operators on ''L''^''p'' spaces with good continuity and boundedness properties. They take their name from the mathematician Viktor Vladimirovich Nemytskii.
==Definition==

Let Ω be a domain (an open and connected set) in ''n''-dimensional Euclidean space. A function ''f'' : Ω × R^''m'' → R is said to satisfy the Carathéodory conditions if
* ''f''(''x'', ''u'') is a continuous function of ''u'' for almost all ''x'' ∈ Ω;
* ''f''(''x'', ''u'') is a measurable function of ''x'' for all ''u'' ∈ R^''m''.
Given a function ''f'' satisfying the Carathéodory conditions and a function ''u'' : Ω → R^''m'', define a new function ''F''(''u'') : Ω → R by
:

F(u)(x) = f \big( x, u(x) \big).

The function ''F'' is called a Nemytskii operator.

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「Nemytskii 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