Approximation of the green operator for linear elliptic differential operators of order four and constant coefficients

Abstract

The Dirichlet problem for A=L₁ L₂ where L₁,L₂ are ellilptic differential operators of order two and constant coefficients is considered. Some representations for the corresponding Green operator G are given. A known representation of the Green operator for the biharmonic problem is included as special case. A sequence of positive compact operators, converging uniformly to G, is indicated.