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In mathematics, Green's identities are a set of three identities in vector calculus. They are named after the mathematician George Green, who discovered Green's theorem. ==Green's first identity== This identity is derived from the divergence theorem applied to the vector field : Let and be scalar functions defined on some region , and suppose that is twice continuously differentiable, and is once continuously differentiable. Then : where is the Laplace operator, is the boundary of region , is the outward pointing unit normal of surface element and is the oriented surface element. This theorem is a special case of the divergence theorem, and is essentially the higher dimensional equivalent of integration by parts with and the gradient of replacing and . Note that Green's first identity above is a special case of the more general identity derived from the divergence theorem by substituting : : 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「Green's identities」の詳細全文を読む スポンサード リンク
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