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Boundary value problems for a class of elliptic operator pencils

R. Denk·R. Mennicken·L. Volevich
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Abstract

In this paper operator pencils $A(x,D,\lambda)$ 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.

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R. Denk, R. Mennicken, L. Volevich. 1999-07-15. Boundary value problems for a class of elliptic operator pencils. https://arxiv.org/abs/math/9907102

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