Weak solutions of $-J_0\partial_t$ on $L^2(S^1,\mathbb{R}^{2n})$ lie in $W^{1,2}$ · Prove2Me

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Weak solutions of $-J_0\partial_t$ on $L^2(S^1,\mathbb{R}^{2n})$ lie in $W^{1,2}$ · Prove2Me