On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results
On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results
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DOI：
10.1007/s00208-016-1487-x
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发表时间：
2016-10
影响因子：
1.4
通讯作者：
S. Dipierro;N. Soave;E. Valdinoci
中科院分区：
文献类型：
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作者：
S. Dipierro;N. Soave;E. Valdinoci
我们考虑无界区域上具有上图性质的非局部方程组。我们证明了对称性、单调性和刚性结果。特别是，我们处理的是半空间，强制性的墓志铭和无限平坦的墓志铭。这些结果可以被视为著名文章(Berestycki等人，Commun Pure Appl Math 50(11)：1089-1111,1997)的非本地对应。
We consider a nonlocal equation set in an unbounded domain with the epigraph property. We prove symmetry, monotonicity and rigidity results. In particular, we deal with halfspaces, coercive epigraphs and epigraphs that are flat at infinity. These results can be seen as the nonlocal counterpart of the celebrated article (Berestycki et al., Commun Pure Appl Math 50(11):1089–1111, 1997).