论文标题
$ \ mathbb {a} $ - quasiconvex函数的部分规律性
Partial Regularity for $\mathbb{A}$-quasiconvex Functionals
论文作者
论文摘要
我们为（局部）普遍的最小化问题建立了部分Hölder规律性，这些问题涉及线性生长的强烈准串联积分，在此，在其中，完整的梯度被一阶均质差异操作员$ \ mathbb {a a}替换为恒定系数。在假设$ \ mathbb {a} $为$ \ mathbb {c} $ - 椭圆形的假设下工作，这是通过调整Gmeineder最近介绍的一种方法来实现的（对称对称的准Quasiconvex的部分规律性BD，J. Math，J。Pures pures pures应用。 BV的规律性，拱门。
We establish partial Hölder regularity for (local) generalised minimisers of variational problems involving strongly quasi-convex integrands of linear growth, where the full gradient is replaced by a first order homogeneous differential operator $\mathbb{A}$ with constant coefficients. Working under the assumption of $\mathbb{A}$ being $\mathbb{C}$-elliptic, this is achieved by adapting a method recently introduced by Gmeineder (Partial Regularity for Symmetric Quasiconvex Functionals on BD, J. Math. Pures Appl. 145 (2021), Issue 9, pp. 83--129) and Gmeineder & Kristensen (Partial regularity for BV Minimizers, Arch. Ration. Mech. Anal. 232 (2019), Issue 3, pp. 1429--1473).
