Commun. Math. Anal.

Volume 21, Number 1 (2018), 54 - 66

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

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

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### 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.