Geodesic
Boundary value problems and layer potentials on manifolds with cylindrical ends
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1151-1197.

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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.”
Classification : 31C12, 35J05, 35S15, 47G30, 58J05, 58J32, 58J40
Keywords: layer potentials; manifolds with cylindrical ends; Dirichlet problem 
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     title = {Boundary value problems and layer potentials on manifolds with cylindrical ends},
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Mitrea, Marius; Nistor, Victor. Boundary value problems and layer potentials on manifolds with cylindrical ends. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1151-1197. http://geodesic.mathdoc.fr/item/CMJ_2007__57_4_a5/