I am looking for a book/paper which has the proof of the RellichNicas identity.
[EDIT by Yemon Choi] It seems that what was meant is "the RellichNecas identity", although the original poster hasn't really clarified or expanded on the request.
I am looking for a book/paper which has the proof of the RellichNicas identity. [EDIT by Yemon Choi] It seems that what was meant is "the RellichNecas identity", although the original poster hasn't really clarified or expanded on the request. 


(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 RellichNecas 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 straightforward 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 $A(\nabla u)\cdot\nabla v \cdot \nabla u$ 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. 


My guessing is that the question is about the socalled RellichNecas identity, named after the late Czech mathematician Jindrich NECAS. See e.g. [C24], [C14], and [C11] in http://dml.cz/bitstream/handle/10338.dmlcz/134050/MathBohem_12920044_8.pdf. 

