P. Baroni

activity

20132026

most citedGlobal estimates for nonlinear parabolic equations

11 citations · 23 across the 8 of their papers we have counts for

collaborators

9 papers

math.AP2026

Partial regularity for vectorial local-nonlocal problems

Carlo Alberto Antonini, Paolo Baroni

We establish sharp interior regularity for solutions to vectorial, nonlinear local-nonlocal systems.

cond-mat.mes-hall2024

Identification by Inelastic X-Ray scattering of bulk alteration of solid dynamics due to Liquid Wetting

M. Warburton, J. Ablett, J. -P. Rueff +3

We examine the influence at room temperature of the deposit of a water layer on the phonon dynamics of a solid. It is shown that the water wetting at the surface of an Alumina mono…

math.AP2017★ 2 cited

Regularity for general functionals with double phase

Paolo Baroni, Maria Colombo, Giuseppe Mingione

We prove sharp regularity results for a general class of functionals of the type $w \mapsto \int F (x, w, D w) d x,$ featuring non-standard growth conditions and non-uniform…

math.AP2017

Existence and boundary regularity for degenerate phase transitions

Paolo Baroni, Tuomo Kuusi, Casimir Lindfors +1

We study the Cauchy-Dirichlet problem associated to a phase transition modeled upon the degenerate two-phase Stefan problem. We prove that weak solutions are continuous up to the p…

math.AP2015

The Cauchy-Dirichlet problem for a general class of parabolic equations

Paolo Baroni, Casimir Lindfors

We prove regularity results such as interior Lipschitz regularity and boundary continuity for the Cauchy-Dirichlet problem associated to a class of parabolic equations inspired by…

math.AP2014

Borderline gradient continuity of minima

Paolo Baroni, Tuomo Kuusi, Giuseppe Mingione

The gradient of any local minimiser of functionals of the type $w \mapsto \int_{Ω} f (x, w, D w) d x + \int_{Ω} w μ d x,$ where $f$ has $p$ -growth, $p > 1$ , and $Ω \subset R^{n}$ , is con…

math.AP2014★ 10 cited

A quantitative modulus of continuity for the two-phase Stefan problem

Paolo Baroni, Tuomo Kuusi, José Miguel Urbano

We derive the quantitative modulus of continuity $ω (r) = [p + ln (\frac{r _{0}}{r})]^{- α (n, p)},$ which we conjecture to be optimal, for solutions of the $p$ …

math.AP2013

Lorentz estimates for obstacle parabolic problems

Paolo Baroni

We prove that the spatial gradient of (variational) solutions to parabolic obstacle problems of p-Laplacian type enjoys the same regularity of the data and of the derivatives of th…

math.AP2013★ 11 cited

Global estimates for nonlinear parabolic equations

Paolo Baroni, Agnese Di Castro, Giampiero Palatucci

We consider nonlinear parabolic equations of the type $u_{t} - d i v a (x, t, D u) = f (x, t) o n Ω_{T} = Ω \times (- T, 0),$ under standard growth conditions on $a$ , with $f$ only assumed to…