Mathematical modelling of an electrolysis process
The paper is devoted to the study of the boundary value problem for an elliptic quasilinear second-order partial differential equation in a multiply connected, bounded plane domain under the assumption that the Dirichlet boundary value conditions on the separate components of the boundary are given up to additive constants. These constants together with the solution of the equation considered are to be determined so as to fulfil the so called trainling conditions. The results have immediate applications...
We present some monotonicity and symmetry results for positive solutions of the equation satisfying an homogeneous Dirichlet boundary condition in a bounded domain . We assume 1 < p < 2 and locally Lipschitz continuous and we do not require any hypothesis on the critical set of the solution. In particular we get that if is a ball then the solutions are radially symmetric and strictly radially decreasing.