$L^p$ regularity of the solution of the heat equation with discontinuous coefficients

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.