Boundary value problems for a class of elliptic operator pencils
Robert Denk, R. Mennicken, L. R. Volevich · arXiv (Cornell University) · 1999
In this paper operator pencils $A(x,D,λ)$ 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.