| [1] Caffarelli L, Silvestre L. An extension problem related to the fractional Laplacian. Comm Partial Differ Equ, 2007, 32: 1245-1260
[2] Blumenthal R M, Getoor R K, Ray D B. On the distribution of first hits for the symmetric stable processes. Tran Amer Math Soc, 1961, 99(3): 540-554
[3] Chen W, Fang Y, Yang R. Semilinear equations involving the fractional Laplacian on domains. Adv Math, 2015, 274: 167-198
[4] Chen W, Li C. Regularity of solutions for a system of integral equation. Comm Pure Appl Anal, 2005, 4: 1-8
[5] Chen W, Li C, Ou B. Qualitative properties of solutions for an integral equation. Disc Cont Dyn Sys, 2005, 12: 347-354
[6] Chen W, Li C, Ou B. Classification of solutions for an integral equation. Comm Pure Appl Math, 2006, 59: 330-343
[7] Applebaum D. Lévy Processes and Stochastic Calculus. Cambridge Studies in Advanced Mathematics, 116. 2nd ed. Cambridge: Cambridge University Press, 2009
[8] Bertoin J. Lévy Processes. Cambridge Tracts in Mathematics, 121. Cambridge: Cambridge University Press, 1996
[9] Cabré X, Tan J. Positive solutions of nonlinear problems involving the square root of the Laplacian. Adv Math, 2010, 224: 2052-2093
[10] Cont R, Tankov P. Financial Modelling with Jump Processes. Boca Raton, Fl: Chapman & Hall/CRC, 2004
[11] Bouchard J P, Georges A. Anomalous diffusion in disordered media, statistical mechanics, models and physical applications. Physics Reports, 1990, 195: 127-293
[12] Constantin P. Euler equations, Navier-Stokes equations and turbulence//Mathematical Foundation of Tur-bulent Viscous Flows. Vol 1871 of Lecture Notes in Math. Berlin: Springer, 2006: 1-43
[13] Caffarelli L, Vasseur A. Drift diffusion equations with fractional diffusion and the quasi-geostrophic equa-tion. Ann Math, 2010, 3: 1903-1930
[14] Fall M M, Weth T. Nonexistence results for a class of fractional elliptic boundary value problems. J Funct Anal, 2012, 263: 2205-2227
[15] Chen W, Ambrosio L D', Li Y. Some Liouville theorems for the fractional Laplacian. Nonlinear Anal: TMA, 2015, 121: 370-381
[16] Chen W, Li C. Methods on Nonlinear Elliptic Equations. AIMS Ser Differ Equ Dyn Syst Vol 4. Amer Inst Math Sci, 2010
[17] Chen W, Li C. Radial symmetry of solutions for some integral systems of Wolff type. Disc Cont Dyn Sys, 2011, 30: 1083-1093
[18] Fall M M. Entire s-harmonic functions are affine. 2014, arXiv:1407.5934
[19] Li D, Zhuo R. An integral equation on half space. Proc Amer Math Soc, 2010, 138: 2779-2791
[20] Zhuo R, Li F, Lv B. Liouville type theorems for Schrdinger system with Navier boundary conditions in a half space. Comm Pure Appl Anal, 2014, 13: 977-990
[21] Zhuo R, Chen W, Cui X, Yuan Z. A Liouville theorem for the fractional Laplacian. Disc Cont Dyn Sys (in press)
[22] Silvestre L. Regularity of the obstacle problem for a fractional power of the Laplace operator. Comm Pure Appl Math, 2007, 60: 67-112
[23] Ma L, Chen D. A Liouville type theorem for an integral system. Comm Pure Appl Anal, 2006, 5: 855-859
[24] Cao L, Chen W. Liouville type theorems for poly-harmonic Navier problems. Disc Cont Dyn Sys, 2013, 33: 3937-3955 |