Monotonicity principles for singular integral equations in Clifford analysis

Abstract

Monotonicity principles can be used to get informations about nonlinear singular integral equations. These results are based on a theorem of Browder and Minty. We consider a family of monotone singular integral operators and associated nonlinear singular integral equations with Nemickii operator in Clifford analysis which has an application to the nonlinear magnetic field equation in the 3-dimensional Euclidean space.