4 papers
Geometric properties of free boundaries in degenerate quenching problems
Damião J. Araújo, Rafayel Teymurazyan, José Miguel Urbano
We study minimizers of non-differentiable functionals modeled on the degenerate quenching problem. Our main result establishes the finiteness of the dimensional Hausdorff m…
On free boundary problems shaped by varying singularities
Damião Araújo, Aelson Sobral, Eduardo V. Teixeira +1
We start the investigation of free boundary variational models featuring varying singularities. The theory depends strongly on the nature of the singular power and how it c…
Interacting free boundaries in obstacle problems
Damião J. Araújo, Rafayel Teymurazyan
We study obstacle problems governed by two distinct types of diffusion operators involving interacting free boundaries. We obtain a somewhat surprising coupling property, leading t…
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…