Integral of $\psi\,\sigma(\partial_s u,\partial_t u)$ for an antisymmetric bilinear form $\sigma$ and a compactly supported weight $\psi$

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Integral of $\psi\,\sigma(\partial_s u,\partial_t u)$ for an antisymmetric bilinear form $\sigma$ and a compactly supported weight $\psi$ · Prove2Me