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KIAM Preprint № 25, Moscow, 2002
Authors: Volevich L.R., Denk R.
Boundary Value Problems for Elliptic Operator Pencils.
In this paper boundary value problems are studied for systems with large parameter, elliptic in the sense of Douglis--Nirenberg. We restrict ourselves on model problems acting in the half-space. It is possible to define parameter-ellipticity for such problems, in particular we formulate Shapiro--Lopatinskii type conditions on the boundary operators. It can be shown that parameter-elliptic boundary value problems are uniquely solvable and that their solutions satisfy uniform a priori estimates in parameter-dependent norms. We essentially use ideas from Newton's polygon method and of Vishik--Lyusternik boundary layer theory.
Publication language: russian
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Volevich L. R.,  KIAM RAS
  • Denk R.