Characterization of the non-homogenous Dirac-harmonic equation

Abstract

Abstract We introduce the non-homogeneous Dirac-harmonic equation for differential forms and characterize the basic properties of solutions to this new type of differential equations, including the norm estimates and the convergency of sequences of the solutions. As applications, we prove the existence and uniqueness of the solutions to a special non-homogeneous Dirac-harmonic equation and its corresponding reverse Hölder inequality.

Keywords

• Dirac-harmonic equation
• Differential forms
• Norm estimates