Regularity of nonlinear equations for fractional Laplacian

  • Xia A
  • Yang J
9Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

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.

Cite

CITATION STYLE

APA

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

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free