The Vishik–Lyusternik method in elliptic problems with a small parameter

Volevich, L.

doi:10.1090/S0077-1554-06-00154-3

The Vishik–Lyusternik method in elliptic problems with a small parameter
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by L. R. Volevich
Translated by: O. A. Khleborodova

Trans. Moscow Math. Soc. 2006, 87-125

DOI: https://doi.org/10.1090/S0077-1554-06-00154-3

Published electronically: December 27, 2006

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Abstract:

We consider boundary value problems where the operator defined in a domain and the boundary operators depend on a small parameter. Elliptic and properly elliptic problems with a small parameter are defined. It is proved that small parameter ellipticity is a necessary and sufficient condition for the existence of a priori estimates that are uniform with respect to the parameter. The proof of uniform estimates is based on the construction of the exponential boundary layer introduced in the classical paper by Vishik and Lyusternik.

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