A class of nonlinear elliptic problems

We obtain a strict coercivity estimate, (generalizing that of T. I. Seidman J. Differential Equations 19 (1975), 242–257] in considering spatial variation) for second order elliptic operators A: u ? ?▽ · γ(·, ▽u) with γ “radial in the gradient” ?γ(·, ξ) = a(·, |ξ|)ξ for ξ ? $\text{R}$^m. The estimate is then applied to obtain existence of solutions of boundary value problems: $\text{?▽ ·}\text{a}\text{?}\text{(·, u, |▽u|) ▽u = f(·, u, ▽u)}$ with Dirichlet conditions.