Constructing graphs over \(\mathbb R^n\) with small prescribed mean-curvature (Q255709)

The authors produce explicit series solutions for prescribed mean curvature problems \[ \pm \nabla \cdot \left( \nabla u / \sqrt{1 \pm |\nabla u|^2}\right) = nH. \] The graph of the unknown function \(u: \mathbb{R}^n \to \mathbb{R}\) is the sought for \(n\)-dimensional hypersurface in the \((n+1)\)-dimensional Euclidean or Minkowski space, with prescribed mean curvature \(H\) with a small norm in the appropriate Hölder space.