arXiv subjects
Publications and source records attributed to Bernard Dacorogna.
We discuss the value of the best constant in Gaffney inequality namely $$ \lVert \nabla ω\rVert_{L^{2}}^{2}\leq C\left( \lVert dω\rVert_{L^{2}}^{2}+\lVert δω\rVert_{L^{2}% }^{2}+\lVert ω\rVert_{L^{2}}^{2}\right) $$ when either $ν\wedgeω=0$ or $ν\,\lrcorner\,ω=0$ on $\partialΩ.$
We study integrals of the form $\int_Ωf\left( dω\right)$, where $1\leq k\leq n$, $f:Λ^{k}\rightarrow\mathbb{R}$ is continuous and $ω$ is a $\left(k-1\right)$-form. We introduce the appropriate notions of convexity, namely ext. one convexity, ext. quasiconvexity and ext. polyconvexity. We study their relations, give several examples and counterexamples. We finally conclude with an application to a minimization problem.
In this article we discuss a generalized Wirtinger inequality.