A Duality Principle

David G. Costa
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David G. Costa: University of Nevada, Las Vegas, Department of Mathematical Sciences

Chapter 7 in An Invitation to Variational Methods in Differential Equations, 2007, pp 63-73 from Springer

Abstract: Abstract A function F: ℝ n → ℝ is said to be convex if, for any u, v ∈ ℝ n and λ ∈ [0, 1], one has $$ F\left( {\left( {1 - \lambda } \right)u + \lambda v} \right) \leqslant \left( {1 - \lambda } \right)F\left( u \right) + \lambda F\left( v \right). $$

Date: 2007
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DOI: 10.1007/978-0-8176-4536-6_7

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