Geodesic
On the boundary values of solutions of second-order elliptic equations
Sbornik. Mathematics, Tome 29 (1976) no. 1, pp. 3-11

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Necessary and sufficient conditions are established under which a solution of an elliptic equation in a ball has a limit in the mean on the boundary sphere. Bibliography: 3 titles. 
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     author = {V. P. Mikhailov},
     title = {On the boundary values of solutions of second-order elliptic equations},
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V. P. Mikhailov. On the boundary values of solutions of second-order elliptic equations. Sbornik. Mathematics, Tome 29 (1976) no. 1, pp. 3-11. http://geodesic.mathdoc.fr/item/SM_1976_29_1_a1/