On lower semicontinuity in the calculus of variations (Q2717343)

The paper is mainly expository in intent. It is addressed to the study of the lower semicontinuity properties of multiple integrals of the calculus of variations of the form NEWLINE\[NEWLINEu\in W^{k,p}(\Omega;\mathbb{R}^d)\mapsto\int_\Omega f(x,u(x),\dots,\nabla^ku(x)) dx,NEWLINE\]NEWLINE where \(\Omega\) is an open bounded subset of \({\mathbf R}^N\) with \(N\geq 1\), and \(k,d\in{\mathbf N}\), \(1\leq p\leq+\infty\). The topology in which lower semicontinuity is considered is the \(W^{k-1,1}(\Omega)\)-one, and coerciveness hypotheses are not necessarily assumed.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00026].