On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results

被引：56

作者：

Dipierro, Serena ^{[1
,2
]}

Soave, Nicola ^{[3
]}

Valdinoci, Enrico ^{[1
,2
,4
,5
]}

机构：

[1] Univ Melbourne, Sch Math & Stat, Swanston St, 813, Parkville, Vic 3010, Australia

[2] Univ Western Australia, Sch Math & Stat, Surling Highway, Perth, WA 6009, Australia

[3] Justus Liebig Univ Giessen, Mathemat Inst, Arndtstrasse,2, D-35392 Giessen, Germany

[4] Weierstrass Inst Angew Anal & Stochastik, Mohrenstrae 39, D-10117 Berlin, Germany

[5] Univ Studi Milano, Dipartimento Matemat, I-20133 Milan, Italy

来源：

MATHEMATISCHE ANNALEN | 2017年 / 369卷 / 3-4期

关键词：

NONLINEAR EQUATIONS; NONNEGATIVE SOLUTIONS; MU-TRANSMISSION; LAPLACIANS; UNIQUENESS; EXISTENCE; SYMMETRY;

D O I：

10.1007/s00208-016-1487-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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).

引用

页码：1283 / 1326

页数：44

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