Positivity for Perturbations of Polyharmonic Operators with Dirichlet Boundary Conditions in Two Dimensions

Abstract

Abstract Higher order elliptic partial differential equations with Dirichlet boundary conditions in general do not satisfy a maximum principle. Polyharmonic operators on balls are an exception. Here it is shown that in IR 2 small perturbations of polyharmonic operators and of the domain preserve the maximum principle. Hence the Green function for the clamped plate equation on an ellipse with small eccentricity is positive.