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A duality theorem for solutions of elliptic equations

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  • Pierre Blanchet

Abstract

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.

Suggested Citation

  • Pierre Blanchet, 1990. "A duality theorem for solutions of elliptic equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 13, pages 1-13, January.
    • Handle: RePEc:hin:jijmms:907527
    DOI: 10.1155/S0161171290000114
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