On the regularity of solutions to elliptic equations

Abstract

We prove that the Meyers’s regularity result for elliptic equations with nonsmooth coefficients and a Dirichlet boundary condition can be generalized for other boundary conditions and for Lipschitz domains. We then apply this result to prove the uniqueness (up to a constant) of the solution of an elliptic equation with a Neumann boundary condition and with right-hand side measure.

Keywords

• regularity
• elliptic equation
• boundary value problem
• lipschitz continuous boundary
• measure data