Denote $I_p[u]:=\int_\Omega |u|^p$ with bounded $\Omega\subset\mathbb{R}^d$ and $0<p<1$.
My question is: Is $I_p$ lower semicontinuous with respect to (strong) $L^2(\Omega)$-topology? I.e., does it hold that $$ u_n\to u \mbox{ in } L^2(\Omega) \qquad\implies\qquad I_p[u] \leq \liminf_{n\to\infty} I_p[u_n] $$ Thank you!