RATE OF CONVERGENCE IN SINGULAR PERTURBATIONS.
KANSAS UNIV LAWRENCE DEPT OF MATHEMATICS
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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.
- Theoretical Mathematics