Resolubility of ideal boundary for nonlinear Dirichlet problems
The paper deals with divergence form quasilinear elliptic differential equations of the form \[ -\text{div } A(x,\nabla u)+B(x,u)=0 \] on a domain \(\Omega\) of \({\mathbb R}^N,\) \(N\geq 2,\) where the functions \(A\) and \(B\) satisfy some natural growth conditions. By the Perron-Wiener-Brelot method, the authors show that the ideal boundary of the Royden type compactification of \(\Omega\) is resoluble with respect to the Dirichlet problem for the above equation.
quasilinear elliptic equations of divergence form
scientific article; zbMATH DE number 1529888