Geodesic
On boundary values of generalized solutions of elliptic equations
Sbornik. Mathematics, Tome 15 (1971) no. 2, pp. 241-260

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It is known that if an analytic function on the disk has exponential growth approaching the boundary, then it has generalized boundary values with which by means of Poisson kernels one can regenerate the function. In this work it is proved that similar properties are also possessed by the generalized solutions of elliptic equations in a bounded region of $n$-dimensional space. The main results were announced earlier (see RZhMat., 1970, 2B409). Bibliography: 18 titles. 
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     author = {Ya. A. Roitberg},
     title = {On boundary values of generalized solutions of elliptic equations},
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Ya. A. Roitberg. On boundary values of generalized solutions of elliptic equations. Sbornik. Mathematics, Tome 15 (1971) no. 2, pp. 241-260. http://geodesic.mathdoc.fr/item/SM_1971_15_2_a4/