Seminari in programmazione durante l'anno accademico 2026-2027
Seminari in programmazione durante l'anno accademico 2026-2027
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5 ottobre 2026 alle ore 12h30 Maicol Caponi
14 settembre 2026 alle ore 12h15 Giacomo Del Nin
Maicol Caponi (Università dell'Aquila)
H-convergence and Gamma-convergence in the Riesz fractional setting: the nonlinear case
5 ottobre 2026 alle ore 12:30: in aula 2BC30
In this talk, we present some recent results on the $H$-convergence of nonlocal elliptic PDEs driven by monotone operators and on the $\Gamma$-convergence of the associated energy functionals, in the framework of the Riesz fractional gradient and divergence.
The first part of the talk is devoted to the relation between local and nonlocal $H$-convergence. We show that, for a suitable class of nonlinear monotone operators, $H$-convergence in the local setting is equivalent to its fractional counterpart. As a consequence, we obtain an $H$-compactness result for the corresponding class of nonlocal operators.
In the second part, we identify a natural subclass of monotone operators associated with energy functionals and investigate the relation between $H$- and $\Gamma$-convergence. We prove that the $\Gamma$-convergence of the associated nonlocal energies is equivalent to the $\Gamma$-convergence of their local counterparts, yielding in particular a $\Gamma$-compactness result. Finally, within this class, we extend the classical equivalence between $H$- and $\Gamma$-convergence to the fractional setting.
This is a joint work with G. C. Brusca (SISSA), A. Carbotti (Università del Salento), A. Maione (Politecnico di Milano), F. Paronetto (Università di Padova).
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Giacomo Del Nin (Max Planck Institute - Leipzig)
Boundary rectifiability and compactness of integral currents via BV functions
14 settembre 2026 alle ore 12:15: in aula 2BC60
We present a proof of the boundary rectifiability theorem for currents that is based on the theory of BV functions. We use a cylindrical projection argument to reduce to the case of top-dimensional currents (i.e., integer-valued BV functions), to which we can apply De Giorgi's structure theorem. As a consequence we also present a proof of the compactness theorem for integral currents that is ultimately based on the BV theory.
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