Seminario del 2024
Giugno
dal giorno
06/06/2024
al giorno
07/06/2024
06/06/2024
al giorno
07/06/2024
Enzo Maria Merlino
Regularity for almost minimizer of a one-phase Bernoulli-type functional in Carnot Groups of step two
Seminario di analisi matematica
The regularity of minimizers of the classical one-phase Bernoulli functional was deeply studied after the pioneering work of Alt and Caffarelli. More recently, the regularity of almost minimizers was investigated as well. We present a regularity result for almost minimizers for a one-phase Bernoulli-type functional in Carnot Groups of step two. Our approach is inspired by the methods introduced by De Silva and Savin in the Euclidean setting. Moreover, some recent intrinsic gradient estimates have been employed. Generalizations to the nonlinear framework will be discussed. Some of the results presented are obtained in collaboration with F. Ferrari (University of Bologna) and N. Forcillo (Michigan State University).