Monotone iterations of two obstacle problems with different operators

Abstract

In this paper we analyze iterations of the obstacle problem for two different operators. We solve iteratively the obstacle problem from above or below for two different differential operators with obstacles given by the previous functions in the iterative process. When we start the iterations with a super or a subsolution of one of the operators this procedure generates two monotone sequences of functions that we show that converge to a solution to the two membranes problem for the two different operators. We perform our analysis in both the variational and the viscosity settings.