54 citations · 68 across the 15 of their papers we have counts for
16 papers
On the existence of solutions to some singular parabolic free boundary problems
Alessandro Audrito, Tomás Sanz-Perela
We construct nonnegative weak solutions to the singular parabolic free boundary problem \[ \partial_t u - Δu = - \frac{\mathrm{d}}{\mathrm{d} u} u_+^γ, \] where , $u_+…
Higher order Schauder estimates for degenerate or singular parabolic equations
Alessandro Audrito, Gabriele Fioravanti, Stefano Vita
In this paper, we complete the analysis initiated in [AFV24] establishing some higher order Schauder estimates () for a a class of parabolic equations…
Schauder estimates for parabolic equations with degenerate or singular weights
Alessandro Audrito, Gabriele Fioravanti, Stefano Vita
We establish some and regularity estimates for a class of weighted parabolic problems in divergence form. The main novelty is that the weights may vanish or exp…
Elliptic regularization of some semilinear parabolic free boundary problems
Alessandro Audrito, Tomás Sanz-Perela
We prove existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. Existence of solutions is obtained in tw…
Regularity theory for fully nonlinear parabolic obstacle problems
Alessandro Audrito, Teo Kukuljan
We study the free boundary of solutions to the parabolic obstacle problem with fully nonlinear diffusion. We show that the free boundary splits into a regular and a singular part:…
Convergence in relative error for the Porous Medium equation in a tube
Alessandro Audrito, Alejandro Gárriz, Fernando Quirós
Given a bounded domain and , we study the long-time behaviour of solutions to the Porous Medium equation (PME) posed in a tube \[ \partial_tu = Δu^m…