[1] Barrios B, Del Pezzo L, Melián J G, Quaas A. A priori bounds and existence of solutions for some nonlocal elliptic problems. Rev Mat Iberoam, 2018, 34:195-220 [2] Bonforte M, Sire Y, Vázquez J L. Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains. Discrete Contin Dyn Syst, 2015, 35:5725-5767 [3] Caffarelli L, Silvestre L. An extension problem related to the fractional Laplacian. Comm Partial Differential Equations, 2007, 32:1245-1260 [4] Caffarelli L, Silvestre L. Regularity theory for fully nonlinear integro-differential equations. Comm Pure Appl Math, 2009, 62:597-638 [5] Caffarelli L, Silvestre L. Regularity results for nonlocal equations by approximation. Arch Ration Mech Anal, 2011, 200:59-88 [6] Caffarelli L, Vasseur A. Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Ann Math, 2010, 171:1903-1930 [7] Cao Y, Wu J, Wang L. Fundamental solutions of a class of homogeneous integro-differential elliptic equations. Discrete Contin Dyn Syst, 2019, 39:1237-1256 [8] Chang K. Methods in Nonlinear Analysis, Springer Monographs in Mathematics. Berlin:Springer-Verlag, 2005 [9] Chen W, Fang Y, Yang R. Loiuville theorems involving the fractional Laplacian on a half space. Adv Math, 2015, 274:167-198 [10] Chen W, Li C. A priori estimates for solutions to nonlinear elliptic equations. Arch Rational Mech Anal, 1993, 122:145-157 [11] Chen W, Li C, Li Y. A direct blowing-up and rescaling argument on nonlocal elliptic equations. Internat J Math, 2016, 27:1650064, 20 pp [12] Chen W, Li C, Ou B. Classification of solutions for an integral equation. Comm Pure Appl Math, 2006, 59:330-343 [13] Chen W, Li Y, Ma P. The Fractional Laplacian. World Scientific Publishing Company, 2020 [14] Cheng T, Huang G, Li C. The maximum principles for fractional Laplacian equations and their applications. Commun Contemp Math, 2017, 19:1750018, 12 pp [15] Constantin P. Euler equations, Navier-Stokes equations and turbulence//Mathematical foundation of turbulent viscous flows. Lecture Notes in Math, 1871. Springer, 2006:1-43 [16] Fall M M. Regularity estimates for nonlocal Schrödinger equations. Discrete Contin Dyn Syst, 2019, 39:1405-1456 [17] de Figueiredo D G, Sirakov B. Liouville type theorems, monotonicity results and a priori bounds for positive solutions of elliptic systems. Math Ann, 2005, 333:231-260 [18] Gidas B, Spruck J. Global and local behavior of positive solutions of nonlinear elliptic equations. Comm Pure Appl Math, 2010, 34:525-598 [19] Gidas B, Spruck J. A priori bounds for positive solutions of nonlinear elliptic equations. Comm Partial Differential Equations, 1981, 6:883-901 [20] Gilbarg D, Trudinger N. Elliptic Partial Differential Equations of Second Order. 2nd ed. Berlin:SpringerVerlag, 1983 [21] Jarohs S, Weth T. Symmetry via antisymmetric maximum principle in nonlocal problems of variable order. Ann Mat Pura Appl, 2016, 195:273-291 [22] Kriventsov D. C1,α interior regularity for nonlinear nonlocal elliptic equations with rough kernels. Comm Partial Differential Equations, 2013, 38:2081-2106 [23] Li C, Wu Z. Radial symmetry for systems of fractional Laplacian. Acta Math Sci, 2018, 38B:1567-1582 [24] Lin L. A priori bounds and existence result of positive solutions for fractional Laplacian systems. Discrete Contin Dyn Syst, 2019, 39:1517-1531 [25] Leite E, Montenegro M. A priori bounds and positive solutions for nonvariational fractional elliptic systems. Differential Integral Equations, 2017, 30:947-974 [26] Polácik P, Quittner P, Souplet P. Singularity and decay estimates in superlinear problems via Liouville-type theorems, I. Elliptic equations and systems. Duke Math J, 2007, 139:555-579 [27] Pivato M, Seco L. Estimating the spectral measure of a multivariate stable distribution via spherical harmonic analysis. J Multivariate Anal, 2003, 87:219-240 [28] Quaas A, Xia A. A Liouville type theorem for Lane-Emden systems involving the fractional Laplacian. Nonlinearity, 2016, 29:2279-2297 [29] Quaas A, Xia A. Liouville type theorems for nonlinear elliptic equations and systems involving fractional Laplacian in the half space. Calc Var Partial Differential Equations, 2015, 52:641-659 [30] Quaas A, Xia A. Existence results of positive solutions for nonlinear cooperative elliptic systems involving fractional Laplacian. Commun Contemp Math, 2018, 20:1750032, 22 pp [31] Silvestre L. Regularity of the obstacle problem for a fractional power of the Laplace operator. Comm Pure Appl Math, 2007, 60:67-112 [32] Servadei R, Valdinoci E. Weak and viscosity solutions of the fractional Laplace equation. Publ Mat, 2014, 58:133-154 [33] Servadei R, Valdinoci E. Lewy-Stampacchia type estimates for variational inequalities driven by (non) local operators. Rev Mat Iberoam, 2013, 29:1091-1126 [34] Wang P, Wang Y. Positive solutions for a weighted fractional system. Acta Math Sci, 2018, 38B:935-949 [35] Wang P, Niu P. Liouville's Theorem for a fractional elliptic system. Discrete Contin Dyn Syst, 2019, 39:1545-1558 [36] Wang P, Niu P. Symmetric properties for fully nonlinear nonlocal system. Nonlinear Anal, 2019, 187:134-146 [37] Yang J, Yu X. Existence of a cooperative elliptic system involving Pucci operator. Acta Math Sci, 2010, 30B:137-147 [38] Zhuo R, Chen W, Cui X, Yuan Z. Symmetry and non-existence of solutions for a nonlinear system involving the fractional Laplacian. Discrete Contin Dyn Syst, 2016, 36:1125-1141 |