Geodesic
$L^p$ regularity of the solution of the heat equation with discontinuous coefficients
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 4, pp. 466-479

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In this paper, we consider the transmission problem for the heat equation on a bounded plane sector in $L^{p}$-Sobolev spaces. By Applying the theory of the sums of operators of Da Prato-Grisvard and Dore-Venni, we prove that the solution can be splited into a regular part in $L^{p}$-Sobolev space and an explicit singular part.
Keywords: transmission heat equation, sums of linear operators, singular behavior, non-smooth domains. 
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     title = {$L^p$ regularity of the solution of the heat equation with discontinuous coefficients},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Selma Kouicem; Wided Chikouche. $L^p$ regularity of the solution of the heat equation with discontinuous coefficients. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 4, pp. 466-479. http://geodesic.mathdoc.fr/item/JSFU_2020_13_4_a8/