Boundary value problems for a class of elliptic operator pencils.
Abstract:
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.
Publication language:russian
Research direction:
Mathematical problems and theory of numerical methods
