Quasilinear elliptic equations with small boundary data

It is shown that if the order of non-uniformity of a quasilinear elliptic equation is h, 1<h≤2, then the critical norm separating existence and non-existence of a solution to the Dirichlet problem with small boundary data is the {Mathematical expression} norm. For 0≤h≤1, existence of a solution is guaranteed without any smallness assumption on the given boundary data, provided that the usual a priori interior gradient bound for solution is available.