Qualitative analysis of very weak solutions to Dirac-harmonic equations

Abstract

Abstract In this paper, we introduce a definition of very weak solutions to the homogenous Dirac-harmonic equations for differential forms. In this setting, applying the Gehring lemma and interpolation theorems, we establish a higher integrability of the Dirac operator based on the very weak solutions and explore the relation between weak solutions and very weak solutions.

Keywords

• Differential forms
• Dirac operator
• Higher integrability
• Very weak solutions