Prelegent: Benjamin Lledos
We want to find a framework in which we can establish the uniqueness of solutions for non-strictly convex problems in the calculus of variations. The main idea is to extend a method devised by Marcellini for a particular scenario. By examining various counterexamples and a simpler case, we demonstrate the uniqueness for two specific problems. These results rely on the global Lipschitz regularity of the minimizers and a comprehensive understanding of the regularity of their level sets.
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