An extension problem for the fractional Laplacian

The extension method transforming the problem of fractional Laplacian \$(-\Delta)^{1/2}\$ to classical Laplacian PDE is a quite well-known approach in dealing with problems with fractional Laplacian. In this talk, I will introduce the paper by Caffarelli and Silvestre in the dealing with fractional with general powers \$s \in (0,1)\$ of fractional Laplacian and also some related properties of integral differential operators and related obstacle problems using this argument.