Let $N_f$ denote the Nemytskii operator and suppose that $u_n\rightharpoonup u$ in $H^1(\mathbb{R}^n)$. It is true that $$ N_f(u_n)\rightharpoonup N_f(u)?$$ And if it is true, in what space we have the weak convergence? Any help or references are well accepted!
2026-03-25 23:37:00.1774481820
Behaviour of Nemytskii operator wtr weak convergence
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