论文标题
关于各种积分最小化的全球规律性：2D中的拆卸型问题以及对一般各向异性设置的扩展
On the global regularity for minimizers of variational integrals: splitting-type problems in 2D and extensions to the general anisotropic setting
论文作者
论文摘要
我们主要讨论在有界Lipschitz域上拆卸型变量积分$ω\ subset \ Mathbb {r}^2 $上的超二次最小化问题，并通过合并适当的权重量的距离来实现了边界数据的距离，从而证明了梯度到边界的更高集成能。作为推论，根据函数$ {\ rm dist}（\ cdot，\ cdot，\ partialω）$量化了本地Hölder系数相对于某些改进的Hölder连续性。结果扩展到各向异性问题，而在自然生长和椭圆状条件下没有分裂结构。在这两种情况下
We mainly discuss superquadratic minimization problems for splitting-type variational integrals on a bounded Lipschitz domain $Ω\subset \mathbb{R}^2$ and prove higher integrability of the gradient up to the boundary by incorporating an appropriate weight-function measuring the distance of the solution to the boundary data. As a corollary, the local Hölder coefficient with respect to some improved Hölder continuity is quantified in terms of the function ${\rm dist}(\cdot,\partial Ω)$. The results are extended to anisotropic problems without splitting structure under natural growth and ellipticity conditions. In both cases we argue with variants of Caccioppoli's inequality involving small weights
