Bounds for Derivatives in the Dirichlet Problem for Poisson’s Equation
James H. Bramble, Lawrence Edward Payne · Journal of the Society for Industrial and Applied Mathematics · 1962
INEQUALITIES ARE DERIVED WHICH LEAD TO POINTWISE BOUNDS FOR DERIVATIVES OF THE SOLUTION OF THE Dirichlet problem for the Poisson equation. We obtain at interior points bounds for first and second derivatives which involve the undifferentiated data providing the boundary data are square integrable and the Laplacian of the function is Holder continuous in D. (Author)