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Let $\Omega$ be a convex open subset of $\mathbb{R}^d$ with a smooth boundary. Is there an example of a one to one and onto mapping of the form $$L^{d+1}(\Omega) \to W^{1,d+1}(\Omega)$$
Let $\Omega$ be a convex open subset of $\mathbb{R}^d$. Is there an example of a one to one and onto mapping of the form $$L^{d+1}(\Omega) \to W^{1,d+1}(\Omega)$$
Let $\Omega$ be a convex open subset of $\mathbb{R}^d$ with a smooth boundary. Is there an example of a one to one and onto mapping of the form $$L^{d+1}(\Omega) \to W^{1,d+1}(\Omega)$$
Is there an example of a one to one and onto mapping between these two spaces?
Let $\Omega$ be a convex open subset of $\mathbb{R}^d$. Is there an example of a one to one and onto mapping of the form $$L^{d+1}(\Omega) \to W^{1,d+1}(\Omega)$$
