Moscow Mathematical Society

Author(s): 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
Posted: 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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Retrieve articles in Transactions of the Moscow Mathematical Society with MSC (2000): 35B40

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: 10.1090/S0077-1554-06-00154-3
PII: S 0077-1554(06)00154-3
Posted: December 27, 2006
Dedicated: To B. P. Paneyakh for his 70th birthday
Copyright of article: Copyright 2006, American Mathematical Society

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ISSN: 1547-738X(e) ISSN: 0077-1554(p)

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