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

@article{Acosta2017AFL, title={A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations}, author={Gabriel Acosta and Juan Pablo Borthagaray}, journal={SIAM J. Numerical Analysis}, year={2017}, volume={55}, pages={472-495} }

- Published 2017 in SIAM J. Numerical Analysis
DOI:10.1137/15M1033952

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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