SOME INTEGRAL REPRESENTATION FORMULAS AND SCHWARZ LEMMAS RELATED TO PERTURBED DIRAC OPERATORS

Abstract

In this paper, we first obtain some integral representations for perturbed Dirac operators by using the fundamental solutions of the modified Helmholtz equation and Clifford calculus approach. Second, based on the exhaustion of arbitrary open subsets and integral representations, we investigate generalized Cauchy type integral representation formulas. Moreover, we establish Schwarz lemmas for the null solutions of perturbed Dirac operators in $\mathbb{R}^{3}$. Finally, as applications, we solve a kind of Dirichlet boundary value problem for perturbed Dirac operators and give the explicit representation of the solution.