The claimed existence of relaxed mean field control equilibria for non-convex first-order problems is invalid as stated.
Semicontinuity, relaxation and integral representation in the calculus of variations, volume 207 ofPitman Research Notes in Mathematics Series
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Relaxed Lagrangian Approach to First-Order Non-Convex Mean Field Type Control Problem
The claimed existence of relaxed mean field control equilibria for non-convex first-order problems is invalid as stated.