5 papers
A numerical scheme for a fully nonlinear free boundary problem
Edgard A. Pimentel, ErcÃlia 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…
Differentiability of solutions for a degenerate fully nonlinear free transmission problem
Edgard A. Pimentel, David Stolnicki
We study a fully nonlinear free transmission problem in the presence of general degeneracy laws. Under minimal conditions on the degeneracy of the model, we establish the different…
Numerical methods for fully nonlinear degenerate diffusions
Edgard A. Pimentel, ErcÃlia Sousa, Ercília Sousa
We propose finite difference methods for degenerate fully nonlinear elliptic equations and prove the convergence of the schemes. Our focus is on the pure equation and a related fre…
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…
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…