Newton's polygon in the theory of singular perturbations of boundary value problems
R. Denk and L. Volevich
Abstract. In this paper we discuss ellipticity conditions for some parameter-dependent boundary value problems which do not satisfy the Agmon-Agranovich-Vishik condition of ellipticity with parameter. The appropriate definition of ellipticity uses the concept of the Newton polygon. For the corresponding boundary value problems with small parameter we construct the formal asymptotic solution, thus explaining the nature of the Shapiro-Lopatinskii condition for these problems.
Functional Differential Eq. 8 (2001), 147-161.
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