Monotone iterations of two obstacle problems with different operators

Abstract

In this paper we analyze iterations of the obstacle problem for two different opera-tors. We solve iteratively the obstacle problem from above or below for two differentdifferential operators with obstacles given by the previous functions in the iterativeprocess. When we start the iterations with a super or a subsolution of one of the opera-tors this procedure generates two monotone sequences of functions that we show thatconverge 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.