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Transactions of the Moscow Mathematical Society

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


Author: L. R. Volevich
Translated by: O. A. Khleborodova
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 67 (2006).
Journal: Trans. Moscow Math. Soc. 2006, 87-125
MSC (2000): Primary 35B40
DOI: https://doi.org/10.1090/S0077-1554-06-00154-3
Published electronically: December 27, 2006
MathSciNet review: 2301592
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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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Additional Information

L. R. Volevich
Affiliation: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 4 Miusskaya Place, Moscow 125047, Russia
Email: volevich@spp.keldysh.ru

DOI: https://doi.org/10.1090/S0077-1554-06-00154-3
Published electronically: December 27, 2006
Dedicated: To B. P. Paneyakh for his 70th birthday
Article copyright: © Copyright 2006 American Mathematical Society

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