Solving the Yamabe Problem by an Iterative Method on a Small Riemannian Domain

We introduce an iterative scheme to solve the Yamabe equation $- a\Delta_{g} u + S u = \lambda u^{p-1}$ on small domains $(\Omega,g)\subset {\mathbb R}^n$ equipped with a Riemannian metric $g$. Thus $g$ admits a conformal change to a constant scalar curvature metric. The proof does not use the traditional functional minimization.