Gradient bounds for harmonic functions lipschitz on the boundary

Abstract

We estimate the magnitude of the gradient of the solution to the Dirichlet problem, with Lipschitz boundary data, for the Laplace equation on a bounded domain ω in . Under certain regularity assumptions on ∂ω, for xεω we established the estimate

where M is the Lipschitz constant of the boundary data

Keywords:

• Harmonic functions
• gradient bounds

AMS:

• 35J50
• 35B30