An $L^{p}$-approach to singular linear parabolic equations in bounded domains

Abstract

Singular means here that the parabolic equation is \textit{not} in normal form neither can it be reduced to such a form. For this class of problems, following the operator approach used in [1], we prove global in time existence and uniqueness theorems related to (spatial) $L^p$-spaces. Various improvements to [2], [3] are given.