3 papers
math.AP2026
Lipschitz regularity for the parabolic obstacle problem
David Jesus, Aelson Sobral, José Miguel Urbano
We study the obstacle problem for the parabolic fractional Laplace equation \[\partial_t u+(-Δ_p)^su = 0\] in the degenerate range . We prove that viscosity soluti…
math.AP2026
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…
math.AP2024
Boundary Estimates for Doubly Nonlinear Parabolic Equations
Ugo Gianazza, David Jesus
We consider non-negative, weak solutions to the doubly nonlinear parabolic equation $$ \partial_t u^q-\mbox{div}(|Du|^{p-2}Du)=0 $$ in the super-critical fast diffusion regime $0<p…