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A Liouville theorem for $\alpha$-harmonic functions in $\mathbb{R}^n_+$
1. | School of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China |
2. | Department of Mathematics, INS and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240 |
3. | Department of Mathematics, Yeshiva University, New York, NY 10033 |
4. | Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China |
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show all references
References:
[1] |
Illinois J. Math., 46 (2002), 541-556. |
[2] |
Milan J. Math., 76 (2008), 27-67.
doi: 10.1007/s00032-008-0090-3. |
[3] |
Nonlinear Anal., 121 (2015), 370-381.
doi: 10.1016/j.na.2014.11.003. |
[4] |
Comm. Pure Appl. Math., 59 (2006), 330-343.
doi: 10.1002/cpa.20116. |
[5] |
Disc. Cont. Dyn. Sys., 12 (2005), 347-354. |
[6] |
Contemp. Math., 528 (2010), 105-114.
doi: 10.1090/conm/528/10417. |
[7] |
M. Fall, Entire s-harmonic functions are affine,, preprint, (). Google Scholar |
[8] |
M. Fall and T. Weth, Monotonicity and nonexistence results for some fractional elliptic problems in the half space,, preprint, (). Google Scholar |
[9] |
Advances in Math., 229 (2012), 2835-2867.
doi: 10.1016/j.aim.2012.01.018. |
[10] |
Translated from the Russian by A. P. Doohovskoy, Die Grundlehren der mathematischen Wissenschaften, Band 180, Springer-Verlag Berlin Heidelberg, New York, 1972.
doi: 10.1007/978-3-642-65183-0. |
[11] |
Analysis, 28 (2008), 449-460.
doi: 10.1524/anly.2008.0928. |
[12] |
J. Differential Equations, 247 (2009), 1479-1504.
doi: 10.1016/j.jde.2009.05.005. |
[13] |
Duke Math. J., 80 (1995), 383-417.
doi: 10.1215/S0012-7094-95-08016-8. |
[14] |
Nonlinear Analysis, 75 (2012), 3036-3048.
doi: 10.1016/j.na.2011.11.036. |
[15] |
Pacific J. Math., 253 (2011), 455-473.
doi: 10.2140/pjm.2011.253.455. |
[16] |
Comm. Pure Appl. Anal., 5 (2006), 855-859.
doi: 10.3934/cpaa.2006.5.855. |
[17] |
Differential & Integral Equations, 9 (1996), 465-479. |
[18] |
Comm. Pure Appl. Math., 38 (1985), 679-684.
doi: 10.1002/cpa.3160380515. |
[19] |
J. Math. Pures Appl., 101 (2014), 275-302.
doi: 10.1016/j.matpur.2013.06.003. |
[20] |
X. Ros-Oton and J. Serra, Boundary regularity for fully nonlinear integro-differential equations,, preprint, (). Google Scholar |
[21] |
Comm. Pure Appl. Math., 60 (2007), 67-112.
doi: 10.1002/cpa.20153. |
[22] |
Proc. Roy. Soc. Edinburgh Sect. A Math., 129 (1999), 649-661.
doi: 10.1017/S0308210500021569. |
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