Geodesic
Asymptotics of the reduced logarithmic capacity of a narrow cylinder
Matematičeskie zametki, Tome 77 (2005) no. 1, pp. 16-27

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We consider the Dirichlet problem for the Laplace operator in the exterior of a narrow infinite cylinder with periodically varying directrix. The solution is sought in the class of functions logarithmically increasing as the distance from the cylinder is increased. The reduced logarithmic capacity is defined as a generalization of the logarithmic capacity (of the outer conformal radius).We construct and justify the asymptotics of the solution of the problem as the ratio of the diameter of the cross-section of the cylinder to its period tends to zero. 
@article{MZM_2005_77_1_a1,
     author = {I. I. Argatov},
     title = {Asymptotics of the reduced logarithmic capacity of a narrow cylinder},
     journal = {Matemati\v{c}eskie zametki},
     pages = {16--27},
     publisher = {mathdoc},
     volume = {77},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_1_a1/}
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I. I. Argatov. Asymptotics of the reduced logarithmic capacity of a narrow cylinder. Matematičeskie zametki, Tome 77 (2005) no. 1, pp. 16-27. http://geodesic.mathdoc.fr/item/MZM_2005_77_1_a1/