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In mathematics, a weak derivative is a generalization of the concept of the derivative of a function (''strong derivative'') for functions not assumed differentiable, but only integrable, i.e. to lie in the L''p'' space . See distributions for an even more general definition. == Definition == Let be a function in the Lebesgue space . We say that in is a ''weak derivative'' of if, : for all infinitely differentiable functions with . This definition is motivated by the integration technique of Integration by parts. Generalizing to dimensions, if and are in the space of locally integrable functions for some open set , and if is a multi-index, we say that is the -weak derivative of if : for all , that is, for all infinitely differentiable functions with compact support in . If has a weak derivative, it is often written since weak derivatives are unique (at least, up to a set of measure zero, see below). 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「weak derivative」の詳細全文を読む スポンサード リンク
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