Abstract
We introduce the boundary integral operator induced from the fractional Laplace equation on the boundary of a bounded smooth domain. For~$\frac 12\lt \alpha \lt 1$, 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 \lt p \lt \infty $. As an application, we demonstrate the existence of the solution of the Dirichlet boundary value problem of the fractional Laplace equation.
Citation
Tongkeun Chang. "Boundary integral operator for the fractional Laplacian on the boundary of a bounded smooth domain." J. Integral Equations Applications 28 (3) 343 - 372, 2016. https://doi.org/10.1216/JIE-2016-28-3-343
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