Let $f \in H^1_0(\Omega)$ and $J$ a bounded, continuous and nonlinear mapping $J:H^1_0(\Omega) \to \mathbb{R}$ such that $|J(f)| \leq C\lVert f \rVert$ for some constant $C$ and $|J(f_n)-J(f)| \leq L \lVert f_n - f \lVert $. Is it possible to prove that $J$ is weakly sequentially lower semicontinuous?
2026-03-27 18:00:06.1774634406
How to prove weak sequential continuity of a continuous, bounded nonlinear mapping?
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