I am looking for a counterexample to Strauss inequality in dimension 1, where it supposedly fails. How can one construct an $H^1(\mathbb{R})$ function which does not decay at infinity, for which for instance $$|u(x)|>C|x|^{-\alpha}||u||_{H^1}?$$ for some $\alpha>0$?
2026-04-01 16:19:27.1775060367
counterexample to strauss inequality
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