Boundary value problems and layer potentials on manifolds with cylindrical ends

Marius Mitrea, Victor Nistor

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

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 [10] and Kral-Wedland [18]. 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."

Original languageEnglish (US)
Pages (from-to)1151-1197
Number of pages47
JournalCzechoslovak Mathematical Journal
Volume57
Issue number4
DOIs
StatePublished - Dec 2007

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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