214 citations · 485 across the 38 of their papers we have counts for
19 papers · 1 filter
Stability for the Surface Diffusion Flow
Antonia Diana, Nicola Fusco, Carlo Mantegazza
We study the global existence and stability of surface diffusion flow (the normal velocity is given by the Laplacian of the mean curvature) of smooth boundaries of subsets of the $…
Semilinear Li & Yau inequalities
Daniele Castorina, Giovanni Catino, Carlo Mantegazza
We derive an adaptation of Li & Yau estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative Ricci tensor. We then apply these estimat…
A matrix Harnack inequality for semilinear heat equations
Giacomo Ascione, Daniele Castorina, Giovanni Catino +1
We derive a matrix version of Li \& Yau--type estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative sectional curvatures and parall…
Global Existence and Stability for the Modified Mullins-Sekerka and Surface Diffusion Flow
Serena Della Corte, Antonia Diana, Carlo Mantegazza
In this survey we present the state of the art about the asymptotic behavior and stability of the modified Mullins--Sekerka flow and the surface diffusion flow of smooth sets, main…
A survey of the elastic flow of curves and networks
Carlo Mantegazza, Alessandra Pluda, Marco Pozzetta
We collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In partic…
A Triviality Result for Semilinear Parabolic Equations
Giovanni Catino, Daniele Castorina, Carlo Mantegazza
We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation \begin{equation*} u_{t}=Δu + |u|^{p} \end{equation*} on co…