Geodesic
On boundary and initial conditions in $\mathscr L_p$, $p>1$, of solutions of parabolic equations
Sbornik. Mathematics, Tome 53 (1986) no. 2, pp. 489-522 
I. M. Petrushko. On boundary and initial conditions in $\mathscr L_p$, $p>1$, of solutions of parabolic equations. Sbornik. Mathematics, Tome 53 (1986) no. 2, pp. 489-522. http://geodesic.mathdoc.fr/item/SM_1986_53_2_a12/
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     title = {On boundary and initial conditions in $\mathscr L_p$, $p>1$, of solutions of parabolic equations},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Necessary and sufficient conditions on the solutions of parabolic equations in a cylinder are established for the existence of limits in $\mathscr L_p$ on the lateral surface of the cylinder and in $\mathscr L_p$ with a weight on its lower base. Bibliography: 9 titles.

[1] 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

[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] Petrushko I. M., “O granichnykh znacheniyakh reshenii ellipticheskikh uravnenii v oblastyakh s lyapunovskoi granitsei”, Matem. sb., 119(161) (1982), 48–77 | MR | Zbl

[4] Petrushko I. M., “O granichnykh znacheniyakh v $\mathcal{L}_p$, $p>1$, reshenii ellipticheskikh uravnenii v oblastyakh s lyapunovskoi granitsei”, Matem. sb., 120(162) (1983), 569–588 | MR | Zbl

[5] Petrushko I. M., “O granichnykh i nachalnykh znacheniyakh reshenii parabolicheskikh uravnenii”, Matem. sb., 106(148), 409–439 | MR | Zbl

[6] Miranda K., Uravneniya s chastnymi proizvodnymi ellipticheskogo tipa, IL, M., 1957

[7] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva P. I., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

[8] Riss F., Sekefalvi-Nad R., Lektsii po funktsionalnomu analizu, IL, M., 1954

[9] Lions Zh.-L., Madzhenes E., Neodnorodnye zadachi i ikh prilozheniya, Mir, M., 1971 | Zbl