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On the Shape of the First Fractional Eigenfunction
Potential Analysis ( IF 1.1 ) Pub Date : 2023-09-05 , DOI: 10.1007/s11118-023-10096-3 Nicola Abatangelo , Sven Jarohs
中文翻译:
关于第一分数本征函数的形状
更新日期:2023-09-06
Potential Analysis ( IF 1.1 ) Pub Date : 2023-09-05 , DOI: 10.1007/s11118-023-10096-3 Nicola Abatangelo , Sven Jarohs
We show that the first eigenfunction of the fractional Laplacian \({\left( -\Delta \right) }^{s}\), \(s\in (1/2,1)\), is superharmonic in the unitary ball up to dimension 11. To this aim, we also rely on a computer-assisted step to estimate a rather complicated constant depending on the dimension and the power s.
中文翻译:
关于第一分数本征函数的形状
我们证明分数拉普拉斯算子的第一个特征函数 \({\left( -\Delta \right) }^{s}\) , \(s\in (1/2,1)\)是酉中的超调和函数球的维度高达 11。为此,我们还依靠计算机辅助步骤来估计一个相当复杂的常数,具体取决于维度和幂s。