6 papers · 1 filter
Well-posedness of Kolmogorov-Fokker-Planck equations with unbounded drift
Francesca Anceschi, Giacomo Ascione, Daniele Castorina +1
We consider Kolmogorov-Fokker-Planck equations with unbounded drift terms which are only measurable in time and locally Hölder continuous in space. In particular, we extend the par…
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…
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…
A Liouville theorem for superlinear heat equations on Riemannian manifolds
Daniele Castorina, Carlo Mantegazza, Berardino Sciunzi
We study the triviality of the solutions of weighted superlinear heat equations on Riemannian manifolds with nonnegative Ricci tensor. We prove a Liouville--type theorem for soluti…
Hopf Lemma and regularity results for quasilinear anisotropic elliptic equations
Daniele Castorina, Giuseppe Riey, Berardino Sciunzi
We consider a class of quasi-linear anisotropic elliptic equations, possibly degenerate or singular, which are of interest in several applications such as computer vision and conti…