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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {I. M. Petrushko},
     title = {On boundary and initial conditions in $\mathscr L_p$, $p>1$, of solutions of parabolic equations},
     journal = {Sbornik. Mathematics},
     pages = {489--522},
     year = {1986},
     volume = {53},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1986_53_2_a12/}
}
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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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[5] Petrushko I. M., “O granichnykh i nachalnykh znacheniyakh reshenii parabolicheskikh uravnenii”, Matem. sb., 106(148), 409–439 | MR | Zbl

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[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