论文标题
Lipschitz边界和非自主积分
Lipschitz bounds and nonautonomous integrals
论文作者
论文摘要
我们为Lipschitz规律性提供了一种通用方法，用于针对表现出不均匀椭圆的大量矢量值，非自主变异问题。这里考虑的功能范围在具有不平衡多项式生长条件的人中，具有快速，指数类型的生长。相对于所考虑的所有数据，获得的结果也很明显，即使在经典的椭圆情况下，也会产生新的，最佳的规律性标准。我们给出了不同类型的非均匀椭圆度的分类，因此确定了适当的条件以获得规律定理。
We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range amongst those with unbalanced polynomial growth conditions to those with fast, exponential type growth. The results obtained are sharp with respect to all the data considered and yield new, optimal regularity criteria even in the classical uniformly elliptic case. We give a classification of different types of nonuniform ellipticity, accordingly identifying suitable conditions to get regularity theorems.
