Geodesic
On boundary values of generalized solutions of elliptic equations
Sbornik. Mathematics, Tome 15 (1971) no. 2, pp. 241-260 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] J. L. Lions, E. Magenes, “Problemi ai limiti non omogenei. III, V”, Ann. Scuola Super. Pisa, ser. III, 15:12 (1961), 39–101 ; 16:1 (1962), 1–44 ; J. Analyse Math. VI, 11 (1963), 165–188 | MR | Zbl | DOI | MR | Zbl

[2] J. L. Lions, E. Magenes, Problemes aux limites non homogenes et applications, v. I, Dunod, Paris, 1968

[3] Z. E. Madzhenes, “Interpolyatsionnye prostranstva i uravneniya v chastnykh proizvodnykh”, Uspekhi matem. nauk, XXI:2(128) (1966), 169–218

[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

[6] Yu. M. Berezanskii, Ya. A. Roitberg, “Teorema o gomeomorfizmakh i funktsiya Grina dlya obschikh ellipticheskikh granichnykh zadach”, Ukr. matem. zh., 19:5 (1967), 3–32 | MR | Zbl

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

[8] Ya. A. Roitberg, “Teorema o gomeomorfizmakh dlya obschikh ellipticheskikh granichnykh zadach s granichnymi usloviyami, ne yavlyayuschimisya normalnymi”, DAN SSSR, 191:6 (1970), 1228–1231 | MR | Zbl

[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

[10] Yu. M. Berezanskii, Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, Naukova dumka, Kiev, 1965 | MR

[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

[13] A. P. Kalderon, “Promezhutochnye prostranstva i interpolyatsiya, kompleksnyi metod”, Matematika, 9:3 (1965), 56–129

[14] S. G. Krein, Yu. I. Petunin, “Shkaly banakhovykh prostranstv”, Uspekhi matem. nauk, XXI:2(128) (1966), 89–168 | MR

[15] M. S. Agranovich, “Ellipticheskie singulyarnye integro-differentsialnye operatory”, Uspekhi matem. nauk, XX:5(125) (1965), 3–120

[16] L. Khërmander, Lineinye differentsialnye operatory s chastnymi proizvodnymi, Mir, Moskva, 1965 | MR

[17] M. Shekhter, “Obschie granichnye zadachi dlya ellipticheskikh uravnenii v chastnykh proizvodnykh”, Matematika, 4:5 (1960), 93–122

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