A note on Meyers’ Theorem in $W^{k,1}$
A note on Meyers’ Theorem in $W^{k,1}$
Lower semicontinuity properties of multiple integrals \[ u\in W^{k,1}(\Omega ;\mathbb {R}^{d})\mapsto \int _{\Omega }f(x,u(x), \cdots ,\nabla ^{k}u(x)) dx\] are studied when $f$ may grow linearly with respect to the highest-order derivative, $\nabla ^{k}u,$ and admissible $W^{k,1}(\Omega ;\mathbb {R}^{d})$ sequences converge strongly in $W^{k-1,1}(\Omega ;\mathbb {R}^{d}).$ It is shown that under …