Equations of mean curvature type on exterior domains (Q1382639)

Results concerning the asymptotic behavior near infinity of solutions of the minimal surface equation in two space dimensions are generalised to more general nonlinear equations of the form \[ \sum^2_{i,j= 1}a_{ij}(\cdot, u,\nabla u)u_{x_ix_j} =0\quad \text{in }\Omega \] under Dirichlet boundary conditions. Here \(\Omega\subset\mathbb{R}^2\) is an exterior domain. The problem is nonuniformly elliptic in the sense of the minimal surface equation. Under suitable assumptions and normalisations the author proves asymptotic expansions for \(u(x)\), \(\nabla u(x)\), \(D^2u(x)\) as \(|x|\to\infty\), existence and/or uniqueness of classical solutions.