Fundamental Solutions of the Laplacian in Dimension 1 and 2
Thierry Goudon · 2016
Fundamental Solutions of the Laplacian in Dimension 1 and 2We saw in section 2.7 that the fundamental solution of the operator -Δ in dimension 3 is 1 4π 1 |x| .More generally, we seek to determine the functions x → E N (x), such that -ΔE N = δ(x = 0) over R N .Evidently, since the Dirac measure appears in this definition, we must work with a concept of weak derivatives.