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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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Sem. Math. Physics Eqs


Some results about the uniqueness of the solutions in the calculus of variations

Prelegent: Benjamin Lledos

2023-05-25 12:30

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.