Corpus ID: 231632082

On the Robin function for the Fractional Laplacian on symmetric domains

  title={On the Robin function for the Fractional Laplacian on symmetric domains},
  author={Alejandro Ortega},
Let 0 < s < 1 and Ω ⊂ R , N > 2s, be a smooth bounded domain. Let GΩ,t(x) the Green function centered at t ∈ Ω of the Fractional Laplacian (−∆) in H 0(Ω). In particular, the fractional operator we deal with is defined through the spectrum of the classical Laplace operator −∆ endowed with homogeneous Dirichlet boundary conditions on ∂Ω. It is known (cf. [6]) that GΩ,t(x) admits the decomposition GΩ,t(x) = G s RN ,t(x)−H s Ω,t(x), where the singular part G RN ,t(x) is given by the fundamental… Expand


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