A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations

  title={A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations},
  author={Gabriel Acosta and Juan Pablo Borthagaray},
  journal={SIAM J. Numerical Analysis},
In this work we deal with the Dirichlet homogeneous problem for the integral fractional Laplacian on a bounded domain Ω ⊂ R. Namely, we deal with basic analytical aspects required to convey a complete Finite Element analysis of the problem (1) { (−∆)u = f in Ω, u = 0 in Ω, where the fractional Laplacian of order s is defined by (−∆)u(x) = C(n, s) P.V. ∫ Rn u(x)− u(y) |x− y|n+2s dy and C(n, s) is a normalization constant. Independently of the Sobolev regularity of the source f , solutions of (1… CONTINUE READING

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