论文标题
沃尔夫的潜力和解决方案的局部行为，以测量数据椭圆形问题的生长
Wolff potentials and local behaviour of solutions to measure data elliptic problems with Orlicz growth
论文作者
论文摘要
我们以非线性操作员的$ a-superharmonic函数为$ a：ω\ times \ times \ mathbb {r}^n \ to \ mathbb {r}^n $具有可测量的依赖性和Orlicz的变量，以$ a-superharmon的功能来建立以$ a $ a-superharmonic函数为单位的估计值。结果是尖锐的，因为从上方和下方从上方和下方的相同电势控制界限。应用它，我们提供了一大堆精确的规律性结果，包括连续性和Hölder连续性，以解决涉及满足自然量表条件的措施的问题的解决方案。最后，我们给出了Hedberg-Wolff定理的变体，内容涉及Orlicz空间的双重表征。
We establish pointwise estimates expressed in terms of a nonlinear potential of a generalized Wolff type for $A$-superharmonic functions with nonlinear operator $A:Ω\times\mathbb{R}^n\to\mathbb{R}^n$ having measurable dependence on the spacial variable and Orlicz growth with respect to the last variable. The result is sharp as the same potential controls bounds from above and from below. Applying it we provide a bunch of precise regularity results including continuity and Hölder continuity for solutions to problems involving measures that satisfies conditions expressed in the natural scales. Finally, we give a variant of Hedberg--Wolff theorem on characterization of the dual of the Orlicz space.
