13 papers · 1 filter
Rectifiability of free boundaries in singular diffusion problems
Rafayel Teymurazyan
For minimizers of a degenerate diffusion functional with a singular reaction term, we prove that the free boundary is -rectifiable. The argument relies on a suitable integra…
Higher Hölder regularity for degenerate elliptic PDEs with data in Morrey spaces
Giuseppe Di Fazio, Rafayel Teymurazyan, José Miguel Urbano
We establish sharp local -regularity for weak solutions to degenerate elliptic equations of -Laplacian type with data in Morrey spaces. The proof relies on the Fefferma…
Improved regularity for a nonlocal dead-core problem
Disson dos Prazeres, Rafayel Teymurazyan, José Miguel Urbano
We obtain improved regularity results for solutions to a nonlocal dead-core problem at branching points. Our approach, which does not rely on the maximum principle, introduces a ne…
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…
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…
The fractional Laplacian: a primer
Rafayel Teymurazyan
In this note we give a glimpse of the fractional Laplacian. In particular, we bring several definitions of this non-local operator and series of proofs of its properties. It is str…