Geodesic
Asymptotics of the solution of Laplace’s equation with third-type boundary conditions on the boundaries of two small holes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 11, pp. 1768-1783

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A boundary value problem for Laplace’s equation in a bounded domain with two small holes is considered. Third-type boundary conditions are set on the boundaries of the holes. A Neumann condition is specified on the outer boundary of the domain. A uniform asymptotic approximation of the solution is constructed and justified up to an arbitrary power of a small parameter. 
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     author = {S. R. Garifullina and E. Yu. Postnikova},
     title = {Asymptotics of the solution of {Laplace{\textquoteright}s} equation with third-type boundary conditions on the boundaries of two small holes},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1768--1783},
     publisher = {mathdoc},
     volume = {53},
     number = {11},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_11_a1/}
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S. R. Garifullina; E. Yu. Postnikova. Asymptotics of the solution of Laplace’s equation with third-type boundary conditions on the boundaries of two small holes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 11, pp. 1768-1783. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_11_a1/