A Liouville theorem for non local elliptic equations
Louis Dupaigne, Yannick Sire · Contemporary mathematics - American Mathematical Society · 2010
Abstract. We prove a Liouville-type theorem for bounded stable solutions v ∈ C 2 (R n) of elliptic equations of the type (−∆) s v = f(v) in R n, where s ∈ (0, 1) and f is any nonnegative function. The operator (−∆) s stands for the fractional Laplacian, a pseudo-differential operator of symbol |ξ | 2s.