Mathematics

Caffarelli and Silvestre show that for 0 < s <1, the s-th power of the positive Laplacian in Rⁿ can be represented as the normal derivative of the extension to the half space in Rⁿ⁺¹ by solution of an elliptic boundary value problem. The case s=1/2 is well-known where the elliptic problem is simply Laplace's equation. For other s, the elliptic equation is degenerate.