RATE OF CONVERGENCE IN SINGULAR PERTURBATIONS.

The paper obtains rate of convergence estimates for solutions of singular perturbations of linear elliptic boundary value problems. The problem can be described as follows. Let D be a domain in R superscript n and let epsilon be a positive real parameter. Consider two boundary value problems on D, epsilon U B w subscript epsilon f, Bu f, where U and B are elliptic differential operators with the order of U greater than the order of B. The problem is to determine in what sense w subscript epsilon converges to u on D as epsilon drops to 0 and to estimate the rate of convergence. This problem is investigated in the present work with the L superscript 2 theory of elliptic partial differential problems.