# Boundary value problems and layer potentials on manifolds with cylindrical ends

Czechoslovak Mathematical Journal (2007)

- Volume: 57, Issue: 4, page 1151-1197
- ISSN: 0011-4642

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topMitrea, Marius, and Nistor, Victor. "Boundary value problems and layer potentials on manifolds with cylindrical ends." Czechoslovak Mathematical Journal 57.4 (2007): 1151-1197. <http://eudml.org/doc/31187>.

@article{Mitrea2007,

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 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.”},

author = {Mitrea, Marius, Nistor, Victor},

journal = {Czechoslovak Mathematical Journal},

keywords = {layer potentials; manifolds with cylindrical ends; Dirichlet problem; layer potentials; manifolds with cylindrical ends; Dirichlet problem},

language = {eng},

number = {4},

pages = {1151-1197},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Boundary value problems and layer potentials on manifolds with cylindrical ends},

url = {http://eudml.org/doc/31187},

volume = {57},

year = {2007},

}

TY - JOUR

AU - Mitrea, Marius

AU - Nistor, Victor

TI - Boundary value problems and layer potentials on manifolds with cylindrical ends

JO - Czechoslovak Mathematical Journal

PY - 2007

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 57

IS - 4

SP - 1151

EP - 1197

AB - 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.”

LA - eng

KW - layer potentials; manifolds with cylindrical ends; Dirichlet problem; layer potentials; manifolds with cylindrical ends; Dirichlet problem

UR - http://eudml.org/doc/31187

ER -

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