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math.AP2024
Regularity in diffusion models with gradient activation
Damião Araújo, Aelson Sobral, Eduardo V. Teixeira
We prove sharp regularity estimates for solutions of highly degenerate fully nonlinear elliptic equations. These are free boundary models in which a nonlinear diffusion process dri…
math.AP2024
Higher regularity of solutions to fully nonlinear elliptic equations
Thialita M. Nascimento, Ginaldo Sá, Aelson Sobral +1
We establish higher regularity properties of solutions to fully nonlinear elliptic equations at interior critical points. The key novelty of our estimates lies in the fact that the…
math.AP2024
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 ch…