Global higher regularity and decay estimates for positive solutions of fractional equations in RN *

Abstract

In the paper, we study the global higher regularity and decay estimates of the positive solutions for the following fractional equations {(−Δ)su+u=|u|p−2uin RN,lim|x|→∞u(x)=0,u∈Hs(RN),(0.1) where s∈(0,1) , N>2s , 2<p<2s∗:=2NN−2s and (−Δ)s is the fractional Laplacian. Let Q be a positive solution of (). We prove that Q∈Ck,γ(RN)∩Hk(RN) and obtain the decay estimates of D k Q as |x|→∞ for all k∈N+ and γ∈(0,1) . The argument relies on the Bessel kernel, comparison principle, Fourier analysis and iteration methods.