8 papers
Fractional -caloric functions are Lipschitz
David Jesus, Aelson Sobral, José Miguel Urbano
We study the parabolic fractional Laplace equation in the degenerate range . We show that weak solutions are Lipschitz continuous…
An -theory for -Schrödinger equations with confinement in measure
Nuno J. Alves, José Miguel Urbano
We consider stationary -Schrödinger equations on the whole space with integrable data and potentials that are confining in measure. We introduce asymptotic energy solutions in…
The two-phase Alt-Phillips problem for quasilinear operators
Yousef Alamri, José Miguel Urbano
We establish interior regularity and optimal growth estimates for sign-changing minimizers of the singular or degenerate quasilinear Alt--Phillips functional throughout the…
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…
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…