Hodge decomposition of variable exponent spaces of Clifford-valued functions and applications to Dirac and Stokes equations

In this paper, we establish a Hodge-type decomposition of variable exponent Lebesgue spaces of Clifford-valued functions, where one of the subspaces is the space of all monogenic Lp(x)-functions. Using this decomposition, we obtain the existence and uniqueness of solutions to the homogeneous A-Dirac equations with variable growth under certain appropriate conditions and to the Stokes equations in the setting of variable exponent spaces of Clifford-valued functions.