论文标题
分数截短的拉普拉斯人：表示公式，基本解决方案和应用
Fractional truncated Laplacians: representation formula, fundamental solutions and applications
论文作者
论文摘要
在本说明中，我们介绍了一些非线性极端非本地算子，这些非本地算子近似于所谓的截短的拉普拉斯人。对于这些操作员，我们构建了代表公式，从而导致滥用符号的构建可以称为“基本解决方案”。反过来，这导致了liouville型结果。兴趣是双重的：一方面，我们希望“理解”定义截短的拉普拉斯主义者非局部版本的正确方法是什么，另一方面，我们介绍了非局部运算符，其非遗传性在一个维度上是在一个维线上的，而与当地情况相差很大，这与结果相差很大，这与前景很明显，而与本地情况有所不同，这是很明显的。令人惊讶的是，对于近似拉普拉斯人的运营商来说，这也是如此。
In this note we introduce some nonlinear extremal nonlocal operators that approximate the, so called, truncated Laplacians. For these operators we construct representation formulas that lead to the construction of what, with an abuse of notation, could be called "fundamental solutions". This, in turn, leads to Liouville type results. The interest is double: on one hand we wish to "understand" what is the right way to define the nonlocal version of the truncated Laplacians, on the other, we introduce nonlocal operators whose nonlocality is on one dimensional lines, and this dramatically changes the prospective, as is quite clear from the results obtained that often differs significantly with the local case or with the case where the nonlocality is diffused. Surprisingly this is true also for operators that approximate the Laplacian.
