Geodesic
Asymptotics of a boundary-value problem solution for the Laplace equation with type changing of the boundary condition on two small sites
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 3, pp. 266-281.

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We consider a harmonic function in a three-dimensional bounded domain. The normal derivative is given on almost the entire boundary, excepting two small sections, on which the value of the function itself is specified. For such a harmonic function, by the method of matching asymptotic expansions, a two-scale asymptotics with respect to a small parameter characterizing the size of the mentioned boundary sections is constructed and justified. The physical application of the obtained decomposition is given.
Keywords: boundary value problem, Laplace equation, asymptotic expansion, mixed problem, small parameter, matching method, electrical resistance. 
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A. A. Ershov; M. I. Rusanova. Asymptotics of a  boundary-value problem solution for the Laplace equation with type changing of the boundary condition on two small sites. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 3, pp. 266-281. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_3_a1/

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