Boundary value problems for a class of elliptic operator pencils

R. Denk, R. Mennicken, and L. Volevich

Abstract. In this paper operator pencils depending polynomially on the spectral parameter are studied which act on a manifold with boundary and satisfy the condition of N -ellipticity with parameter, a generalization of the notion of ellipticity with parameter as introduced by Agmon and Agranovich-Vishik. Sobolev spaces corresponding to a Newton polygon are defined and investigated; in particular it is possible to describe  their trace spaces. With respect to these spaces, an a priori estimate  holds for the Dirichlet boundary value problem connected with an N-elliptic pencil, and a right parametrix is constructed.

Integral Equations Operator Theory 38 (2000), 410-436.

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