Ros-Oton, Serra: Understanding singularitiesin free boundary problems

Ros-Oton, Xavier and Serra, Joaquim:
Understanding singularitiesin free boundary problems
Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana Serie 1 4 (2019), fasc. n.2, p. 107-118, (English)
pdf (675 Kb), djvu (286 Kb). | MR 3965683

Sunto

I problemi di frontiera libera sono quelli descritti da EDP che mostrano interfacce o frontiere a priori sconosciuti (liberi). L'esempio più classico è lo scioglimento del ghiaccio in acqua (problema di Stefan). In questo caso, la frontiera libera è l'interfaccia solido-liquido tra acqua e ghiaccio. Una sfida matematica centrale in questo contesto è comprendere la regolarità e le singolarità delle frontiere libere. In questo articolo introduciamo questo argomento presentando alcuni risultati classici di Luis Caffarelli, oltre ad alcuni importanti lavori recenti dovuti ad Alessio Figalli e collaboratori.

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Referenza completa

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Referenze Bibliografiche