The exterior Dirichlet problem for quasi-linear elliptic equations with small boundary data

It is shown that if the order of non-uniformity of a quasi-linear elliptic equation is h,12,then the critical norm separating existence and non-existence of a bounded solution to the exterior Dirichlet problem with small boundary data is the C^0,2(h–1)/h norm. For 0h1,existence of a bounded solution is guaranteed without any smallness assumption on the given boundary data.More precise information is given for the special case of the minimal surface equation.