A $W^{1,p}$ solution of $\partial_s u+J(u)\,\partial_t u=0$ with $p>2$ is of class $W^{2,p}$ near every point

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A $W^{1,p}$ solution of $\partial_s u+J(u)\,\partial_t u=0$ with $p>2$ is of class $W^{2,p}$ near every point · Prove2Me