Journal of Prime Research in Mathematics

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

$$^{1}$$Corresponding Author: nabhatti35@yahoo.com
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 $$L^{∞}$$-norm, then the gradients of the solutions of the corresponding obstacle problem are close in the weighted $$L^{2}$$ -norm.