On Weak Solutions to Dirac-Harmonic Equations for Differential Forms

摘要

In this paper, we consider the Dirac-harmonic equations for differential forms with Dirichlet boundary data in weak sense. Using the Hodge-decomposition theory of differential forms and Browder-Minty theory of monotone operators, the existence is obtained. According to the Poincar,-type inequality of Dirac-Sobolev space, we get the higher integrability.