Lower Semicontinuity of Integral Functionals
Lower Semicontinuity of Integral Functionals
It is shown that the integral functional $I(y,z) = {\smallint _G}f(t,y(t),z(t))d\mu$ is lower semicontinuous on its domain with respect to the joint strong convergence of ${y_k} \to y$ in ${L_p}(G)$ and the weak convergence of ${z_k} \to z$ in ${L_p}(G)$, where $1 \leq p \leq \infty$ and $1 \leq q …