M. Carducci - B. Velichkov
Existence and regularity in the fully nonlinear one-phase free boundary problem
Published Paper
Inserted: 22 jan 2025
Last Updated: 12 sep 2026
Journal: SIAM J. Math. Anal.
Year: 2025
Doi: https://doi.org/10.1137/25M1739273
Abstract:
We consider viscosity solution to one-phase free boundary problems for general fully nonlinear operators and free boundary condition depending on the normal vector. We show existence of viscosity solutions via the Perron's method and we prove $C^{2,\alpha}$ regularity of flat free boundaries via a quadratic improvement of flatness. Finally, we obtain the higher regularity of the free boundary via an hodograph transform.