Regularity of nonlinear equations for fractional Laplacian

Abstract

In this paper, we prove that any H s (Ω) solution u of the problem (0.1) (−Δ) s u = f (u) in Ω, u = 0 on ∂Ω, belongs to L ∞ (Ω) for the nonlinearity of f (t) being subcritical and critical. This implies that the solution u is classical if f (t) is C 1,γ for some 0 < γ < 1.