Geodesic
Asymptotic behaviour of bounded controls for a~singular elliptic problem in a~domain with a~small cavity
Sbornik. Mathematics, Tome 189 (1998) no. 11, pp. 1611-1642

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The problem of optimal control of solutions of an elliptic equation in a domain with a small cavity is discussed. Uniform asymptotic formulae for the solutions are obtained up to an arbitrary degree of the small parameter by the method of matching asymptotic expansions. Other aspects of the same problem have been considered by Kapustyan. 
@article{SM_1998_189_11_a1,
     author = {A. R. Danilin},
     title = {Asymptotic behaviour of bounded controls for a~singular elliptic problem in a~domain with a~small cavity},
     journal = {Sbornik. Mathematics},
     pages = {1611--1642},
     publisher = {mathdoc},
     volume = {189},
     number = {11},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_11_a1/}
}
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A. R. Danilin. Asymptotic behaviour of bounded controls for a~singular elliptic problem in a~domain with a~small cavity. Sbornik. Mathematics, Tome 189 (1998) no. 11, pp. 1611-1642. http://geodesic.mathdoc.fr/item/SM_1998_189_11_a1/