论文标题
关于非标准椭圆操作员有限解决方案的点的注释
A note on the point-wise behaviour of bounded solutions for a non-standard elliptic operator
论文作者
论文摘要
在此简短的说明中，我们讨论了解决方案的本地Hölder连续性，以解决类型$ \ sum_ {i = 1}^s \ partial_ {ii} u++++++ \ sum_ {i = s+ 1}^n \ partial_i \ partial_i \ bigG（a_i（x，x，x，u，u，\ nabl u）= 0， ω\ subset \ subset \ mathbb {r}^n $和$ 1 \ leq s \ leq n-1 $，其中每个操作员$ a_i $作为单向$ p $ -laplacian，$ 1 <p <2 $ and $ 1 <p <2 $和超临界条件$ p+（n-s）（n-s）（p-2）（p-2）> 0 $ 0 $ 0 $ 0 $ 0。我们表明，在没有解决方案的连续性的情况下，可以证明Harnack不平等现象，这反过来意味着解决方案的连续性。
In this brief note we discuss local Hölder continuity for solutions to anisotropic elliptic equations of the type $ \sum_{i=1}^s \partial_{ii} u+ \sum_{i=s+1}^N \partial_i \bigg(A_i(x,u,\nabla u) \bigg) =0,$ for $x \in Ω\subset \subset \mathbb{R}^N$ and $1\leq s \leq N-1$, where each operator $A_i$ behaves directionally as the singular $p$-Laplacian, $1< p < 2$ and the supercritical condition $p+(N-s)(p-2)>0$ holds true. We show that the Harnack inequality can be proved without the continuity of solutions and that in turn this implies Hölder continuity of solutions.
