Lᵖ Regularity of the Solution of the Heat Equation with Discontinuous Coefficients

Abstract

In this paper, we consider the transmission problem for the heat equation on a bounded plane sector in Lᵖ-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 Lp-Sobolev space and an explicit singular part