Calculus of Variations and Geometric Measure Theory

M. Carducci - B. Velichkov

Existence and regularity in the fully nonlinear one-phase free boundary problem

created by carducci on 22 Jan 2025

[BibTeX]

preprint

Inserted: 22 jan 2025

Year: 2025

ArXiv: 2501.12101 PDF

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.