## Communications in Mathematical Analysis

- 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

#### 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.

#### Article information

**Source**

Commun. Math. Anal., Volume 21, Number 1 (2018), 54-66.

**Dates**

First available in Project Euclid: 12 September 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.cma/1536717642

**Mathematical Reviews number (MathSciNet)**

MR3845083

**Zentralblatt MATH identifier**

07002171

**Subjects**

Primary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] 35J25: Boundary value problems for second-order elliptic equations 35A05 35D10

**Keywords**

Neumann problem Poisson equation Maxwell-Stokes equation existence of a weak solution regularity of a weak solution

#### Citation

Aramaki, Junichi. Existence and Regularity for the Neumann Problem to the Poisson Equation and an Application to the Maxwell-Stokes Type Equation. Commun. Math. Anal. 21 (2018), no. 1, 54--66. https://projecteuclid.org/euclid.cma/1536717642