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It is given that $k>\frac{m}{2}$.
Question: Let $f_{\lambda}$ be the minimizer of the functional corresponding to $\lambda$. I want to prove that the map $h:\mathbb{R}^+ \to \mathbb{R}$ defined as $$h(\lambda) = \frac{\|f_{\lambda}\|_{L^2}}{\|\nabla^kf_{\lambda}\|_{L^2}}$$
is a contracti...
