论文标题
在对称的层压凸和Quasiconvex船体上，用于二维的共面N-Well问题
On the symmetric lamination convex and quasiconvex hull for the coplanar n-well problem in two dimensions
论文作者
论文摘要
我们研究了二维线性弹性中$ n $ well问题的一些特定情况。 Assuming that every well in $\mathcal{U}\subset\mathbb{R}^{2\times 2}_\text{sym}$ belong to the same two-dimensional affine subspace, we characterize the symmetric lamination convex hull $L^e(\mathcal{U})$ for any number of wells in terms of the symmetric lamination convex $ \ Mathcal {U} $中包含的所有三孔子集的船体。对于一个四孔组的家庭，两对井是排名一的兼容，我们表明对称的层压凸凸和Quasiconvex船体重合，但严格包含在其凸壳$ C（\ Mathcal {u}）中。我们将此结果扩展到$ n $井的某些特定配置。大多数证据都是建设性的，我们也提出了明确的例子。
We study some particular cases of the $n$-well problem in two-dimensional linear elasticity. Assuming that every well in $\mathcal{U}\subset\mathbb{R}^{2\times 2}_\text{sym}$ belong to the same two-dimensional affine subspace, we characterize the symmetric lamination convex hull $L^e(\mathcal{U})$ for any number of wells in terms of the symmetric lamination convex hull of all three-well subsets contained in $\mathcal{U}$. For a family of four-well sets where two pairs of wells are rank-one compatible, we show that the symmetric lamination convex and quasiconvex hulls coincide, but are strictly contained in its convex hull $C(\mathcal{U})$. We extend this result to some particular configurations of $n$ wells. Most of the proofs are constructive, and we also present explicit examples.
