Geodesic
On boundary values of solutions of elliptic equations degenerating on the boundary
Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 243-262 Cet article a éte moissonné depuis la source Math-Net.Ru

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Necessary and sufficient conditions are established for the existence, on the domain's boundary, of a limit in $\mathscr L_p$, $p>1$, of solutions of second order elliptic equations having Tricomi type degeneracy on the boundary. Solvability of the Dirichlet problem for such an equation in spaces of type $W^1_{p,\mathrm{loc}}$ is proved. Bibliography: 9 titles. 
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     title = {On boundary values of solutions of elliptic equations degenerating on the boundary},
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I. M. Petrushko. On boundary values of solutions of elliptic equations degenerating on the boundary. Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 243-262. http://geodesic.mathdoc.fr/item/SM_1989_64_1_a14/

[1] Mikhailov V. P., “O granichnykh znacheniyakh reshenii ellipticheskikh uravnenii vtorogo poryadka v oblastyakh s gladkoi granitsei”, Matem. sb., 101(143) (1976), 163–188

[2] Mikhailov Yu. A., “O granichnykh znacheniyakh v $L_p$, $p>1$, reshenii lineinogo ellipticheskogo uravneniya vtorogo poryadka”, Differents. uravneniya, 19:2 (1983), 318–337 | MR

[3] Ladyzhenskaya O. A., Uraltseva N. P., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964 | MR

[4] Guschin A. K., Mikhailov V. P., “O granichnykh znacheniyakh v $L_p$, $p>1$, reshenii ellipticheskikh uravnenii”, Matem. sb., 108(150) (1979), 3–21 | MR | Zbl

[5] Koshelev P. N., “Apriornye otsenki v $L_p$ i obobschennye resheniya ellipticheskikh uravnenii i sistem”, UMN, 13:4 (1958), 29–88 | MR

[6] Keldysh M. V., “O nekotorykh sluchayakh vyrozhdeniya uravnenii ellipticheskogo tipa na granitse oblasti”, DAN SSSR, 77:2 (1951), 181–183

[7] Oleinik O. A. Radkevich E. V., “Uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Matematicheskii analiz. 1969, VINITI, M., 1971, 7–252 | MR

[8] Vragov V. N., “Analitichnost resheniya zadachi $E$ dlya odnogo vyrozhdayuschegosya ellipticheskogo uravneniya”, Differents. uravneniya, 10:1 (1974), 36–40 | MR | Zbl

[9] Tersenov S. A., “Ob analitichnosti reshenii odnogo klassa differentsialnykh uravnenii, vyrozhdayuschikhsya na granitse”, DAN SSSR, 228:6 (1976), 1294–1297 | MR | Zbl