A duality theorem for solutions of elliptic equations
Pierre Blanchet · International Journal of Mathematics and Mathematical Sciences · 1990
Let L be a second order linear partial differential operator of elliptic type on a domain Ω of ℝ m with coefficients in C ∞ ( Ω ). We consider the linear space of all solutions of the equation L u = 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.