Chang, Tongkeun Boundary integral operator for the fractional Laplacian on the boundary of a bounded smooth domain. (English) Zbl 1361.30063 J. Integral Equations Appl. 28, No. 3, 343-372 (2016). Summary: We introduce the boundary integral operator induced from the fractional Laplace equation on the boundary of a bounded smooth domain. For \(\frac 12<\alpha<1\), we show the bijectivity of the boundary integral operator \(S_{2\alpha}:L^p(\partial \Omega)\to H^{2\alpha -1}_p(\partial \Omega)\) for \(1<p<\infty\). As an application, we demonstrate the existence of the solution of the Dirichlet boundary value problem of the fractional Laplace equation. Cited in 1 Document MSC: 30E25 Boundary value problems in the complex plane 45P05 Integral operators Keywords:boundary integral operator; layer potential; fractional Laplacian PDFBibTeX XMLCite \textit{T. Chang}, J. Integral Equations Appl. 28, No. 3, 343--372 (2016; Zbl 1361.30063) Full Text: DOI arXiv Euclid