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International Journal of Mathematics and Mathematical Sciences - Volume 2003 2003, Issue 6, Pages 327-395



Krasnoyarsk State University, pr. Svobodnyi 79, Krasnoyarsk 660041, Russia

Universität Potsdam, Institut für Mathematik, Postfach 60 15 53, Potsdam 14415, Germany

Received 10 June 2002

Copyright © 2003 Hindawi Publishing Corporation. 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 Abe a determined or overdetermined elliptic differentialoperator on a smooth compact manifold X. Write 𝒮A𝒟for the space of solutions of the system Au=0 in a domain 𝒟⋐X. Using reproducing kernels related to variousHilbert structures on subspaces of 𝒮A𝒟, we showexplicit identifications of the dual spaces. To prove theregularity of reproducing kernels up to the boundary of 𝒟, wespecify them as resolution operators of abstract Neumannproblems. The matter thus reduces to a regularity theorem for theNeumann problem, a well-known example being the∂¯-Neumann problem. The duality itself takes placeonly for those domains 𝒟 which possess certain convexityproperties with respect to A.





Author: A. Shlapunov and N. Tarkhanov

Source: https://www.hindawi.com/



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