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Zeitschrift für Analysis und ihre Anwendungen

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Volume 3, Issue 4, 1984, pp. 315–328
DOI: 10.4171/ZAA/110

Published online: 1984-08-31

Interior Estimates for Singularly Perturbed Problems

Dietrich Göhde

The solution of the Dirichlet problem for a singularly perturbed elliptic differential equation $\epsilon L_1u + L_0u = h$ of order $2m$ converges, for $\epsilon \to 0$, outside of the boundary layer uniformly to a solution of the degenerate elliptic equation $L_0w = h$ of lower order. It is shown in the case of order zero of $L_0$ this assertion may be proved immediately, i.e., without the usual construction of boundary layer terms, but rather elementary and on weak smoothness conditions with respect to the boundary of the domain.

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Göhde Dietrich: Interior Estimates for Singularly Perturbed Problems. Z. Anal. Anwend. 3 (1984), 315-328. doi: 10.4171/ZAA/110