Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Annales Polonici Mathematici / All issues

Abstract

The study of the equation $(L_2L_1)^* h= 0$ or of the equivalent system $L_{2}^{\ast }h_{2}=-h_{1}$, $L_{1}^{\ast }h_{1}=0$, where $L_{j}$ $(j=1,2)$ is a second order elliptic differential operator, leads us to the following general framework: Starting from a biharmonic space, for example the space of solutions $(u_{1},u_{2})$ of the system $L_{1}u_{1}=-u_{2}$, $L_{2}u_{2}=0$, $L_{j}$ $(j=1,2)$ being elliptic or parabolic, and by means of its Green pairs, we construct the associated adjoint biharmonic space which is in duality with the initial one.