Suppose f is a map defined between $W_0^{1,p}(\Omega)$ and $L^{p'}(\Omega)$ as follows - $u \mapsto |\nabla u|^{p-1}$. Is the range of this map weakly closed in $L^{p'}$?.
2025-01-13 02:23:17.1736734997
Is the image of gradient map from Sobolev space to Lebesgue space weakly closed?
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