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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb. (N.S.), 1971 Volume 86(128), Number 2(10), Pages 248–267 (Mi sm3294)

This article is cited in 17 papers

On boundary values of generalized solutions of elliptic equations

Ya. A. Roitberg


Abstract: 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.

UDC: 517.946

MSC: Primary 35J40; Secondary 46E35

Received: 20.10.1970


 English version:
Mathematics of the USSR-Sbornik, 1971, 15:2, 241–260

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