11 papers
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…
Sharp regularity for singular obstacle problems
Damião J. Araújo, Rafayel Teymurazyan, Vardan Voskanyan
We obtain sharp local regularity of solutions for singular obstacle problems, Euler-Lagrange equation of which is given by …
An optimal Liouville theorem for the porous medium equation
Damião J. Araújo, Rafayel Teymurazyan
Under a sharp asymptotic growth condition at infinity, we prove a Liouville type theorem for the inhomogeneous porous medium equation, provided it stays universally close to the he…