CONTINUOUS DEPENDENCE OF THE SOLUTIONS OF ELUPTIC BWNOARY VALUE PROBLEMS ON THE COEFFICIENTS, RIGHT HAND SIDES AND BOUNDARY CONDITIONS

Abstract

A stability theory is developed for second order elliptic boundary value problems by considering perturbations of the coefficients, right hand sides and boundary conditions. Systematic use is made of suitable a priori estimates in order to obtain stability results for the solutions in Sobolev spaces of arbitrary order and therefore also for classical solutions.