Dual Extremum Principles for Non-negative Unsymmetric Operators

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Abstract
Dual extremum principles are constructed for non-negative unsymmetric operator equations. The theory is in terms of functional-valued linear operators defined on an infinite-dimensional space which need not even be normed. Saddle operators and saddle functional are constructed as essential ingredients. An extension to affine sub-spaces required for certain partial differential equations is included. New dual extremum principles for versions of the heat equation and the wave equation are stated in illustration.

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