Hodge-type Decomposition for Time-dependent First-order Parabolic Operators with Non-constant Coefficients:The Variable Exponent Case

摘要

In this paper we present a Hodge-type decomposition for variable exponent spaces. More concretely, we address some time-dependent parabolic firstorder partial differential operators with non-constant coefficients, where one of the components is the kernel of the parabolic-type Dirac operator. This decomposition is presented over different types of domains in the n-dimensional Euclidean space R~n. The case of the time-dependent Schr?dinger operator is included as a special case within this context.