Geodesic
Asymptotic behavior of the solution of the Neumann problem with a delta-like boundary function
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 3, pp. 479-485

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A uniform asymptotic expansion is found for the integral $\iint_S\nabla^2 u\, dx\,dy$, where $u$ is the solution of the Neumann problem with a delta-function-like derivative on the boundary. A physics application of the result is discussed. 
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     author = {A. A. Ershov},
     title = {Asymptotic behavior of the solution of the {Neumann} problem with a delta-like boundary function},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_3_a6/}
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A. A. Ershov. Asymptotic behavior of the solution of the Neumann problem with a delta-like boundary function. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 3, pp. 479-485. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_3_a6/