Boundary value problems for a class of elliptic operator pencils

Details Boundary value problems for a class of elliptic operator pencils Boundary value problems for a class of elliptic operator pencils

1999-07-15

arxiv.org/abs/math/9907102v1

Mathematics

Analysis of PDEs

40 pages

Scientific paper

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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