A convex functional is a type of functional that satisfies the property of convexity, meaning that for any two points in its domain and any number between 0 and 1, the functional evaluated at a weighted average of those two points is less than or equal to the weighted average of the functional's values at those points. This property is crucial in the context of variational principles, as it often guarantees the existence and uniqueness of solutions to optimization problems in physics and mechanics.
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