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11 papers · 2 filters
Self-improving property of the fast diffusion equation
Ugo Gianazza, Sebastian Schwarzacher
We show that the gradient of the -power of a solution to a singular parabolic equation of porous medium-type (also known as fast diffusion equation), satisfies a reverse Hölder…
-solutions of the Navier-Stokes equation with fractional Brownian noise
Bendetta Ferrario, Christian Olivera
We study the Navier-Stokes equations on a smooth bounded domain ( or 3), under the effect of an additive fractional Brownian noise. We show local existe…
A variational approach to the mean field planning problem
Carlo Orrieri, Alessio Porretta, Giuseppe Savaré
We investigate a first-order mean field planning problem of the form \begin{equation} \left\lbrace\begin{aligned} -\partial_t u + H(x,Du) &= f(x,m) &&\text{in } (0,T)\times \mathbb…
A Boundary Estimate for Degenerate Parabolic Diffusion Equations
Ugo Gianazza, Naian Liao
We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to degenerate parabolic equations of -laplacian type. The…
On a Cheeger--Kohler-Jobin inequality
Ilaria Lucardesi, Dario Mazzoleni, Berardo Ruffini
We discuss the minimization of a Kohler-Jobin type scale-invariant functional among open, convex, bounded sets, namely among open convex bounde…
On a Navier-Stokes-Allen-Cahn model with inertial effects
Gianluca Favre, Giulio Schimperna
A mathematical model describing the flow of two-phase fluids in a bounded container is considered under the assumption that the phase transition process is influenced by inerti…