In this paper, we study the local behavior of nonnegative solutions of fractional semi-linear equations
Révisé le :
Accepté le :
DOI : 10.1016/j.anihpc.2020.07.003
Mots-clés : Isolated singularities, Monotonicity formula, Positive solutions, Fractional semi-linear elliptic equations
@article{AIHPC_2021__38_2_403_0, author = {Yang, Hui and Zou, Wenming}, title = {On isolated singularities of fractional semi-linear elliptic equations}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {403--420}, publisher = {Elsevier}, volume = {38}, number = {2}, year = {2021}, doi = {10.1016/j.anihpc.2020.07.003}, mrnumber = {4211991}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2020.07.003/} }
TY - JOUR AU - Yang, Hui AU - Zou, Wenming TI - On isolated singularities of fractional semi-linear elliptic equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2021 SP - 403 EP - 420 VL - 38 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2020.07.003/ DO - 10.1016/j.anihpc.2020.07.003 LA - en ID - AIHPC_2021__38_2_403_0 ER -
%0 Journal Article %A Yang, Hui %A Zou, Wenming %T On isolated singularities of fractional semi-linear elliptic equations %J Annales de l'I.H.P. Analyse non linéaire %D 2021 %P 403-420 %V 38 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2020.07.003/ %R 10.1016/j.anihpc.2020.07.003 %G en %F AIHPC_2021__38_2_403_0
Yang, Hui; Zou, Wenming. On isolated singularities of fractional semi-linear elliptic equations. Annales de l'I.H.P. Analyse non linéaire, mars – avril 2021, Tome 38 (2021) no. 2, pp. 403-420. doi : 10.1016/j.anihpc.2020.07.003. http://www.numdam.org/articles/10.1016/j.anihpc.2020.07.003/
[1] On higher dimensional singularities for the fractional Yamabe problem: a non-local Mazzeo-Pacard program, Duke Math. J., Volume 168 (2019) no. 17, pp. 3297-3411 | MR
[2] A gluing approach for the fractional Yamabe problem with isolated singularities, J. Reine Angew. Math., Volume 763 (2020), pp. 25-78 | DOI | MR
[3] Existence of positive weak solutions for fractional Lane-Emden equations with prescribed singular set, Calc. Var. Partial Differ. Equ., Volume 57 (2018) no. 6 | MR
[4] Local behavior of solutions of some elliptic equations, Commun. Math. Phys., Volume 108 (1987), pp. 177-192 | DOI | MR | Zbl
[5] Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations, Invent. Math., Volume 106 (1991) no. 3, pp. 489-539 | DOI | MR | Zbl
[6] Nonlinear equations for fractional Laplacians, I: regularity, maximum principles, and Hamiltonian estimates, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 31 (2014), pp. 23-53 | DOI | Numdam | MR | Zbl
[7] Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Commun. Pure Appl. Math., Volume 42 (1989), pp. 271-297 | DOI | MR | Zbl
[8] Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities, Arch. Ration. Mech. Anal., Volume 213 (2014) no. 1, pp. 245-268 | DOI | MR | Zbl
[9] Nonlocal minimal surfaces, Commun. Pure Appl. Math., Volume 63 (2010), pp. 1111-1144 | DOI | MR | Zbl
[10] An extension problem related to the fractional Laplacian, Commun. Partial Differ. Equ., Volume 32 (2007) no. 8, pp. 1245-1260 | DOI | MR | Zbl
[11] Fractional Laplacian in conformal geometry, Adv. Math., Volume 226 (2011), pp. 1410-1432 | DOI | MR | Zbl
[12] On the asymptotic symmetry of singular solutions of the scalar curvature equations, Math. Ann., Volume 313 (1999), pp. 229-245 | DOI | MR | Zbl
[13] Classification of isolated singularities of nonnegative solutions to fractional semi-linear elliptic equations and the existence results, J. Lond. Math. Soc. (2), Volume 97 (2018), pp. 196-221 | DOI | MR
[14] A direct method of moving planes for the fractional Laplacian, Adv. Math., Volume 308 (2017), pp. 404-437 | DOI | MR
[15] On the fractional Lane-Emden equation, Trans. Am. Math. Soc., Volume 369 (2017), pp. 6087-6104 | DOI | MR
[16] Isolated singularities for a semilinear equation for the fractional Laplacian arising in conformal geometry, Rev. Mat. Iberoam., Volume 34 (2018) no. 4, pp. 1645-1678 | DOI | MR
[17] Delaunay-type singular solutions for the fractional Yamabe problem, Math. Ann., Volume 369 (2017), pp. 597-626 | DOI | MR
[18] Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. Math., Volume 136 (2012), pp. 521-573 | DOI | MR | Zbl
[19] Semilinear elliptic equations for the fractional Laplacian with Hardy potential | arXiv | DOI
[20] Unique continuation property and local asymptotics of solutions to fractional elliptic equations, Commun. Partial Differ. Equ., Volume 39 (2014), pp. 354-397 | DOI | MR | Zbl
[21] Further studies of Emden's and similar differential equations, Q. J. Math., Oxf. Ser., Volume 2 (1931), pp. 259-288 | DOI | Zbl
[22] Uniqueness of radial solutions for the fractional Laplacian, Commun. Pure Appl. Math., Volume 69 (2016), pp. 1671-1726 | DOI | MR
[23] Global and local behavior of positive solutions of nonlinear elliptic equations, Commun. Pure Appl. Math., Volume 34 (1981), pp. 525-598 | DOI | MR | Zbl
[24] Singular solutions of fractional order conformal Laplacians, J. Geom. Anal., Volume 22 (2012), pp. 845-863 | DOI | MR | Zbl
[25] Fractional conformal Laplacians and fractional Yamabe problems, Anal. PDE, Volume 6 (2013), pp. 1535-1576 | DOI | MR | Zbl
[26] On local behavior of singular positive solutions to nonlocal elliptic equations, Calc. Var. Partial Differ. Equ., Volume 56 (2017) no. 1 | MR
[27] On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions, J. Eur. Math. Soc., Volume 16 (2014), pp. 1111-1171 | DOI | MR | Zbl
[28] Existence theorems of the fractional Yamabe problem, Anal. PDE, Volume 11 (2018) no. 1, pp. 75-113 | DOI | MR
[29] Refined asymptotics for constant scalar curvature metrics with isolated singularities, Invent. Math., Volume 135 (1999) no. 2, pp. 233-272 | DOI | MR | Zbl
[30] Isolated singularities in semilinear problems, J. Differ. Equ., Volume 38 (1980), pp. 441-450 | DOI | MR | Zbl
[31] Singularity and decay estimates in superlinear problems via Liouville-type theorems, Duke Math. J., Volume 139 (2007), pp. 555-579 | DOI | MR | Zbl
[32] Local behavior of solutions of quasi-linear equation, Acta Math., Volume 111 (1964), pp. 247-302 | DOI | MR | Zbl
[33] Uniform Hölder bounds for strongly competing systems involving the square root of the Laplacian, J. Eur. Math. Soc., Volume 15 (2016), pp. 2865-2924 | DOI | MR
[34] On the uniqueness of solutions of a nonlocal elliptic system, Math. Ann., Volume 365 (2016), pp. 105-153 | DOI | MR
Cité par Sources :
This work was supported by NSFC (11771234, 11926323).