Work

Existence and Regularity in the Fully Nonlinear One-Phase Free Boundary Problem

Year: 2026

Type: article

Abstract: . We consider viscosity solutions to one-phase free boundary problems for general fully nonlinear operators and free boundary condition depending on the normal vector. We show the existence of viscosity solutions via Perron’s method and we prove [Formula: see text] regularity of flat free boundaries via a quadratic improvement of flatness. Finally, we obtain the higher regularity of the free boundary via a hodograph transform.

Source: SIAM Journal on Mathematical Analysis

DOI: 10.1137/25m1739273

Authors: Matteo Carducci, Bozhidar Velichkov

Institutions: Scuola Normale Superiore, University of Pisa

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Ministero dell’Istruzione, dell’Università e della Ricerca, Università di Pisa, H2020 European Research Council

Awards: Variational approach to the regularity of the free boundaries, G7967740883, G856286776