Geodesic
Understanding singularitiesin free boundary problems
Matematica, cultura e società, Série 1, Tome 4 (2019) no. 2, pp. 107-118

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Free boundary problems are those described by PDEs that exhibit a priori unknown (free) interfacesor boundaries. The most classical example is the melting of ice to water (the Stefan problem). In this case, the freeboundary is the liquid-solid interface between ice and water. A central mathematical challenge in this context is to understand the regularity and singularities of free boundaries. In this paper we provide a gentle introduction to this topic by presenting some classical results of Luis Caffarelli, as well as some important recent works due to Alessio Figalli and collaborators. 
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     author = {Ros-Oton, Xavier and Serra, Joaquim},
     title = {Understanding singularitiesin free boundary problems},
     journal = {Matematica, cultura e societ\`a},
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     year = {2019},
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     language = {en},
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Ros-Oton, Xavier; Serra, Joaquim. Understanding singularitiesin free boundary problems. Matematica, cultura e società, Série 1, Tome 4 (2019) no. 2, pp. 107-118. http://geodesic.mathdoc.fr/item/RUMI_2019_1_4_2_a5/