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math.AP2024
Generic regularity of free boundaries in the obstacle problem for the fractional Laplacian
Matteo Carducci, Roberto Colombo
We establish generic regularity results of free boundaries for solutions of the obstacle problem for the fractional Laplacian . We prove that, for almost every obstacle, th…
math.AP2024
An epiperimetric inequality for odd frequencies in the thin obstacle problem
Matteo Carducci, Bozhidar Velichkov
We prove for the first time an epiperimetric inequality for the thin obstacle Weiss' energy with odd frequencies and we apply it to solutions to the thin obstacle problem with gene…