REGULARITY OF NONLINEAR EQUATIONS FOR FRACTIONAL LAPLACIAN.

In this paper, we prove that any H^s (Ω) solution u of the problem s (0.1) (-Δ)^su = f(u) in Ω,u = 0 on ∂ύ, 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. [ABSTRACT FROM AUTHOR]