Stability estimate for the multidimensional elliptic obstacle problem with respect to the obstacle function

Abstract

The stability estimate of the energy integral established by Danelia, Dochviri and Shashiashvili [1] for the solution of the multidimensional obstacle problem in case of the Laplace operator is generalized to the case of arbitrary linear second order self-adjoint elliptic operator. This estimate asserts that if two obstacle functions are close in the L∞L∞-norm, then the gradients of the solutions of the corresponding obstacle problem are close in the weighted L2L2 -norm.