Geodesic
Mixed problem for a harmonic function
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 7, pp. 1094-1106 
A. A. Ershov. Mixed problem for a harmonic function. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 7, pp. 1094-1106. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_7_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A harmonic function is considered in a three-dimensional bounded domain. Its normal derivative is given on nearly the entire boundary of the domain, while the value of the harmonic function is specified on the remaining small portion. The method of matched asymptotic expansions is used to construct a complete uniform asymptotic expansion of the function in powers of a small parameter characterizing the size of the boundary portion with a specified function value. The asymptotic expansion is rigorously substantiated.

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