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IEVref:102-05-32ID:
Language:enStatus: Standard
Term: first Green formula
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Definition: identity resulting from the divergence theorem applied to the vector field f 1 grad f 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgadaWgaaWcba GaaGymaaqabaGccaaMc8ocbeGaa83zaiaa=jhacaWFHbGaa8hzaiaa ykW7caWGMbWaaSbaaSqaaiaaikdaaeqaaaaa@3FC0@ , where f1 and f2 are two scalar fields given at each point of a three-dimensional domain V limited by a closed surface S

V ( grad f 1 grad f 2 + f 1 Δ f 2 ) dV= S f 1 grad f 2 e n dA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaapmfabaWaaeWaae aaieqajugqbiaa=DgacaWFYbGaa8xyaiaa=rgakiaaykW7caWGMbWa aSbaaSqaaKqzaeGaaGymaaWcbeaakiabgwSixNqzafGaa83zaiaa=j hacaWFHbGaa8hzaOGaaGPaVlaadAgadaWgaaWcbaqcLbqacaaIYaaa leqaaOGaey4kaSIaamOzamaaBaaaleaajugabiaaigdaaSqabaGcca aMc8ocdaGae4hLdqKaaGjcVlaadAgadaWgaaWcbaqcLbqacaaIYaaa leqaaaGccaGLOaGaayzkaaaaleaajugabiaabAfaaSqab0Gaey4kIi Vaey4kIiVaey4kIipajugqbiaacsgakiaadAfacqGH9aqpdaWdwbqa aiaadAgadaWgaaWcbaqcLbqacaaIXaaaleqaaaqaaKqzaeGaae4uaa WcbeqdcqWIs4U0cqGHRiI8cqGHRiI8aOGaaGPaVNqzafGaa83zaiaa =jhacaWFHbGaa8hzaOGaaGPaVlaadAgadaWgaaWcbaqcLbqacaaIYa aaleqaaOGaeyyXICTaaCyzamaaBaaaleaajugabiaab6gaaSqabaqc LbuacaGGKbGccaWGbbaaaa@7D05@

where dV is the volume element, endA is the vector surface element and Δ is the Laplacian operator

Note 1 to entry: In English the first Green formula is sometimes called “first Green theorem” or “first Green identity”.


Publication date:2008-08
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Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO
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