ap.analysis of pdes - Rellich-Necas identity

(Boo! I tried to post this in a comment to Ady, but the HTML Math won't parse right. So here goes. Sorry about the really long equation being broken up not very neatly.)

Googling Rellich-Necas turns up a bunch of recent papers by LUIS ESCAURIAZA in which the identities are used. But as far as I can tell the identity is just a simple differential equality obtained from symbolic manipulation of terms. The following seems to be a straight-forward version of the identity: let $A = (A_{ij})$ be a symmetric bilinear form (with variable coefficients) on R^N, $v$ a vector field, $u$ a function, and $delta$ denoting the Euclidean divergence, we have

$delta( A(nabla u,nabla u) v) = 2 delta( v(u) A(nabla u)) + delta(v) A(nabla u,nabla u)$
$- 2A(nabla u) cdot nabla v cdot nabla u - 2 v(u) delta(A(nabla u)) + v(A)(nabla u,nabla u)$

Where $v(u)$ is the partial derivative of $u$ in the direction of $v$, and $A(nabla u)cdotnabla v cdot nabla u$ is, in coordinates, $partial_i u A_{ij} partial_j v_k partial_k u$ with implied summation, and $v(A)$ is the symmetric bilinear form obtained by taking the $v$ partial derivative of the coefficients of $A$.

Verifying that the identity is true should just be a basic application of multivariable calculus.

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