On isolated singularities of fractional semi-linear elliptic equations

Hui Yang1, Wenming Zou2
1Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China
2Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Tài liệu tham khảo

Ao, 2019, On higher dimensional singularities for the fractional Yamabe problem: a non-local Mazzeo-Pacard program, Duke Math. J., 168, 3297, 10.1215/00127094-2019-0034

Ao, 2020, A gluing approach for the fractional Yamabe problem with isolated singularities, J. Reine Angew. Math., 763, 25, 10.1515/crelle-2018-0032

Caffarelli, 1989, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Commun. Pure Appl. Math., 42, 271, 10.1002/cpa.3160420304

Caffarelli, 2014, Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities, Arch. Ration. Mech. Anal., 213, 245, 10.1007/s00205-014-0722-4

Caffarelli, 2007, An extension problem related to the fractional Laplacian, Commun. Partial Differ. Equ., 32, 1245, 10.1080/03605300600987306

Chang, 2011, Fractional Laplacian in conformal geometry, Adv. Math., 226, 1410, 10.1016/j.aim.2010.07.016

Chen, 2018, Classification of isolated singularities of nonnegative solutions to fractional semi-linear elliptic equations and the existence results, J. Lond. Math. Soc. (2), 97, 196, 10.1112/jlms.12104

Dávila, 2017, On the fractional Lane-Emden equation, Trans. Am. Math. Soc., 369, 6087, 10.1090/tran/6872

DelaTorre, 2018, Isolated singularities for a semilinear equation for the fractional Laplacian arising in conformal geometry, Rev. Mat. Iberoam., 34, 1645, 10.4171/rmi/1038

Fall

Fall, 2014, Unique continuation property and local asymptotics of solutions to fractional elliptic equations, Commun. Partial Differ. Equ., 39, 354, 10.1080/03605302.2013.825918

Fowler, 1931, Further studies of Emden's and similar differential equations, Q. J. Math., Oxf. Ser., 2, 259, 10.1093/qmath/os-2.1.259

Frank, 2016, Uniqueness of radial solutions for the fractional Laplacian, Commun. Pure Appl. Math., 69, 1671, 10.1002/cpa.21591

Gidas, 1981, Global and local behavior of positive solutions of nonlinear elliptic equations, Commun. Pure Appl. Math., 34, 525, 10.1002/cpa.3160340406

González, 2013, Fractional conformal Laplacians and fractional Yamabe problems, Anal. PDE, 6, 1535, 10.2140/apde.2013.6.1535

Jin, 2017, On local behavior of singular positive solutions to nonlocal elliptic equations, Calc. Var. Partial Differ. Equ., 56, 10.1007/s00526-016-1102-8

Jin, 2014, On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions, J. Eur. Math. Soc., 16, 1111, 10.4171/JEMS/456

Kim, 2018, Existence theorems of the fractional Yamabe problem, Anal. PDE, 11, 75, 10.2140/apde.2018.11.75

Lions, 1980, Isolated singularities in semilinear problems, J. Differ. Equ., 38, 441, 10.1016/0022-0396(80)90018-2

Poláčik, 2007, Singularity and decay estimates in superlinear problems via Liouville-type theorems, Duke Math. J., 139, 555, 10.1215/S0012-7094-07-13935-8

Terracini, 2016, Uniform Hölder bounds for strongly competing systems involving the square root of the Laplacian, J. Eur. Math. Soc., 15, 2865, 10.4171/JEMS/656