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.
CITATION STYLE
Xia, A., & Yang, J. (2013). Regularity of nonlinear equations for fractional Laplacian. Proceedings of the American Mathematical Society, 141(8), 2665–2672. https://doi.org/10.1090/s0002-9939-2013-11734-x
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