Geodesic
On boundary values of generalized solutions of elliptic equations
Sbornik. Mathematics, Tome 15 (1971) no. 2, pp. 241-260 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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[4] Ya. A. Roitberg, “Ellipticheskie zadachi s neodnorodnymi granichnymi usloviyami i lokalnoe povyshenie gladkosti vplot do granitsy obobschennykh reshenii”, DAN SSSR, 157:4 (1964), 798–801 | MR | Zbl

[5] Ya. A. Roitberg, “Teorema o gomeomorfizmakh, osuschestvlyaemykh s ellipticheskimi operatorami, i lokalnoe povyshenie gladkosti obobschennykh reshenii”, Ukr. matem. zh., 17:5 (1965), 122–129 | MR | Zbl

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[7] Ya. A. Roitberg, “Teoremy o gomeomorfizmakh, osuschestvlyaemykh ellipticheskimi operatorami”, DAN SSSR, 180:3 (1968), 542–545 | MR | Zbl

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[9] Ya. A. Roitberg, “Teoremy o gomeomorfizmakh i formula Grina dlya obschikh ellipticheskikh granichnykh zadach s granichnymi usloviyami, ne yavlyayuschimisya normalnymi”, Matem. sb., 83(125) (1970), 181–213 | MR | Zbl

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[11] Ya. A. Roitberg, “O granichnykh znacheniyakh obobschennykh reshenii ellipticheskikh uravnenii”, DAN SSSR, 188:1 (1969), 41–44 | MR | Zbl

[12] M. Schechter, “On $L^p$ estimates and regularity. I, II”, Amer. J. Math., 85:1 (1963), 1–13 | DOI | MR | Zbl

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[18] Ya. A. Roitberg, Teoriya razreshimosti v obobschennykh funktsiyakh obschikh granichnykh zadach dlya ellipticheskikh uravnenii, Dissertatsiya, Voronezh, 1969