Geodesic
Boundary value problems and layer potentials on manifolds with cylindrical ends
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1151-1197 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.”
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 
@article{CMJ_2007_57_4_a5,
     author = {Mitrea, Marius and Nistor, Victor},
     title = {Boundary value problems and layer potentials on manifolds with cylindrical ends},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1151--1197},
     year = {2007},
     volume = {57},
     number = {4},
     mrnumber = {2357585},
     zbl = {1174.31002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a5/}
}
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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/