Global L^∞ and decay estimate for fractional p-Laplacian equations in Ds,p(N)

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