[Dottorcomp] Seminari di Matematica Applicata, 02/09/2025, José Miguel Urbano

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 2 Settembre 2025, alle ore 15 precise, presso l'aula Beltrami del
Dipartimento di Matematica,

José Miguel Urbano (KAUST and University of Coimbra)

terrà un seminario dal titolo:

Borderline regularity in singular free boundary problems.

Abstract: We address the borderline regularity of local minimizers of
energy functionals under minimal assumptions on the potential term. When
the potential is merely bounded and measurable, we show that sign-changing
minimizers are Log-Lipschitz continuous, which is optimal in this general
setting. In the one-phase case, however, we obtain gradient bounds along
the free boundary, revealing a structural gain in regularity. Most notably,
we prove that minimizers are continuously differentiable along the free
boundary if the potential is continuous, thereby identifying a sharp
threshold for differentiability in terms of the regularity of the potential.

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https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/