Items for "Dirichlet boundary conditions"

Separating positivity and regularity for fourth order Dirichlet problems in 2d-domains

The main result in this paper is that the solution operator for the bi-Laplace problem with zero Dirichlet boundary conditions on a bounded smooth 2d-domain can be split in a positive part and a possibly negative part which both satisfy the zero boundary condition...

Keywords: biharmonic operator, Dirichlet boundary conditions, Green function estimates, positivity, maximum principle