International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 1, Pages 73-85
doi:10.1155/S0161171290000114
A duality theorem for solutions of elliptic equations
Department of Mathematics, Indiana University, Bloomington 47405, Indiana, USA
Received 11 April 1989
Copyright © 1990 Pierre Blanchet. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let L be a second order linear partial differential operator of elliptic type on a domain Ω of ℝm with coefficients in C∞(Ω). We consider the linear space of all solutions of the equation Lu=0 on Ω with the topology of uniform convergence on compact subsets and describe the topological dual of this space. It turns out that this dual may be identified with the space of solutions of an adjoint equation “near the boundary” modulo the solutions of this adjoint equation on the entire domain.