3 papers
math.NA2025
A numerical scheme for a fully nonlinear free boundary problem
Edgard A. Pimentel, Ercília Sousa
We propose a numerical method to approximate viscosity solutions of fully nonlinear free transmission problems. The method discretises a two-layer regularisation of a PDE, involvin…
math.AP2024
Fully nonlinear free boundary problems: optimal boundary regularity beyond convexity
Damião J. Araújo, Andreas Minne, Edgard A. Pimentel
We study a general class of elliptic free boundary problems equipped with a Dirichlet boundary condition. Our primary result establishes an optimal -regularity estimate fo…
math.AP2024
Boundary regularity for a fully nonlinear free transmission problem
David Jesus, Edgard A. Pimentel, David Stolnicki
We examine boundary regularity for a fully nonlinear free transmission problem. We argue using approximation methods, comparing the operators driving the problem with a limiting pr…