By Joseph John Kohn

Part rationalization of significant contemporary paintings, and half advent to a few of the ideas of recent partial differential equations, this monograph is a self-contained exposition of the Neumann challenge for the Cauchy-Riemann complicated and likely of its purposes. The authors end up the most life and regularity theorems intimately, assuming just a wisdom of the elemental thought of differentiable manifolds and operators on Hilbert house. They speak about functions to the idea of numerous complicated variables, learn the linked advanced at the boundary, and description different innovations appropriate to those difficulties. In an appendix they boost the practical research of differential operators when it comes to Sobolev areas, to the level it's required for the monograph.

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