Existence and Regularity for the Neumann Problem to the Poisson Equation and an Application to the Maxwell-Stokes Type Equation

Abstract

In this paper, we consider the Neumann problem for the Laplace operator with a given data containing a divergence of a vector field. We demonstrate the existence and regularity of a weak solution. As an application, we consider the existence and regularity of a weak solution in regard to the Maxwell-Stokes type equation.