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Boundary integral operator for the fractional Laplacian on the boundary of a bounded smooth domain. (English) Zbl 1361.30063

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.

MSC:

30E25 Boundary value problems in the complex plane
45P05 Integral operators
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