Global L∞ and decay estimate for fractional p-laplacian equations in Ds,p(RN)

Abstract

In this paper we present a new global L∞-estimate for solutions u ∈ Ds,p(RN ) of the fractional p-Laplacian equation u ∈ Ds,p(RN ) : (− p)su = f (x, u) in RN , of the form u ∞ ≤ C ( u β) for someβ > p, where : R + → R + is a data independent function with lims→0+ (s) = 0. The obtained L∞-estimate is used to prove a decay estimate based on pointwise estimates in terms of nonlinearWolff potentials. Taking advantage of both the L∞ and decay estimate we prove a Brezis-Nirenberg type result regarding Ds,2(RN ) versus Cb RN , 1 + |x|N−2s local minimizers.