Seminario

December 4th, 2023, 12:30pm. Location: Aula Gris 2, ICMAT.

Enzo Maria Merino (U. Bologna)

Title: Intrinsic Lipschitz regularity for almost minimizer of a one-phase Bernoulli-type functional in Carnot Groups of step 2.

Abstract: 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. Some generalizations will be discussed. Some of the results presented are obtained in collaboration with F. Ferrari (University of Bologna) and N. Forcillo (Michigan State University) and will be part of my PhD thesis.