Reliable Solution of a Quasilinear Nonpotential Elliptic Problem of a Nonmonotone Type with Respect to the Uncertainty in Coefficients

Abstract

AbstractA quasilinear elliptic equation with mixed nonlinear boundary conditions is considered, where the admissible coefficients are given in a certain interval. We are looking for maximal values of the solution with respect to the set of admissible coefficients. The existence of a maximal solution is proven both in the continuous and in a discretized formulation. Some convergence analysis is also presented