Boundary value problems and layer potentials on manifolds with cylindrical ends

Title:

Boundary value problems and layer potentials on manifolds with cylindrical ends

Creator:

Mitrea, Marius and Nistor, Victor

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:493c01f7-ece9-4549-a290-5cce60c50d30
uuid:493c01f7-ece9-4549-a290-5cce60c50d30

Subject:

layer potentials, manifolds with cylindrical ends, and Dirichlet problem

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We study the method of layer potentials for manifolds with boundary and cylindrical ends. The fact that the boundary is non-compact prevents us from using the standard characterization of Fredholm or compact pseudo-differential operators between Sobolev spaces, as, for example, in the works of Fabes-Jodeit-Lewis and Kral-Wedland . We first study the layer potentials depending on a parameter on compact manifolds. This then yields the invertibility of the relevant boundary integral operators in the global, non-compact setting. As an application, we prove a well-posedness result for the non-homogeneous Dirichlet problem on manifolds with boundary and cylindrical ends. We also prove the existence of the Dirichlet-to-Neumann map, which we show to be a pseudodifferential operator in the calculus of pseudodifferential operators that are “almost translation invariant at infinity”.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1151-1197

Source:

Czechoslovak Mathematical Journal | 2007 Volume:57 | Number:4

Harvested from:

CDK

Metadata only:

false