∭
where dV is the volume element, endA is the vector surface element and Δ is the Laplacian operator
Note 1 to entry: The second Green formula is symmetric with respect to f1 and f2.
∭ V ( f 1 Δ f 2 − f 2 Δ f 1 ) dV= ∯ S ( f 1 grad f 2 − f 2 grad f 1 ) ⋅ e n dA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaapmfabaWaaeWaae aacaWGMbWaaSbaaSqaaKqzaeGaaGymaaWcbeaakiaayIW7imaacqWF uoarcaaMi8UaamOzamaaBaaaleaajugabiaaikdaaSqabaGccqGHsi slcaWGMbWaaSbaaSqaaKqzaeGaaGOmaaWcbeaakiaayIW7cqWFuoar caaMi8UaamOzamaaBaaaleaajugabiaaigdaaSqabaaakiaawIcaca GLPaaaaSqaaiaabAfaaeqaniabgUIiYlabgUIiYlabgUIiYdqcLbua caGGKbGccaWGwbGaeyypa0Zaa8GvaeaadaqadaqaaiaadAgadaWgaa WcbaqcLbqacaaIXaaaleqaaOGaaGPaVJqabKqzafGaa43zaiaa+jha caGFHbGaa4hzaOGaaGPaVlaadAgadaWgaaWcbaqcLbqacaaIYaaale qaaOGaeyOeI0IaamOzamaaBaaaleaajugabiaaikdaaSqabaGccaaM c8EcLbuacaGFNbGaa4NCaiaa+fgacaGFKbGccaaMc8UaamOzamaaBa aaleaajugabiaaigdaaSqabaaakiaawIcacaGLPaaaaSqaaKqzaeGa ae4uaaWcbeqdcqWIs4U0cqGHRiI8cqGHRiI8aOGaeyyXICTaaCyzam aaBaaaleaajugabiaab6gaaSqabaqcLbuacaGGKbGccaWGbbaaaa@81AA@