preprint

Inserted: 21 jun 2023
Last Updated: 22 aug 2024

Journal: Calculus of Variations and Partial Differential Equations
Volume: 63
Pages: Art. 183.
Year: 2024
Doi: https://doi.org/10.1007/s00526-024-02789-3

Abstract:

We show that any minimizer of the well-known ACF functional (for the p-Laplacian) constitutes a viscosity solution. This allows us to establish a uniform flatness decay at the two-phase free boundary points to improve the flatness, which boils down to C^{1,\eta} regularity of the flat part of the free boundary. This result, in turn, is used to prove the Lipschitz regularity of minimizers by a dichotomy argument. It is noteworthy that the analysis of branch points is also included.