5 papers
Unified growth rates for operator semigroups under generalized Kreiss conditions
Filippo Dell'Oro, Alberto Farina, Vittorino Pata
In this note we establish a unified growth rate for the operator norm of -semigroups on Hilbert spaces whose generators satisfy the generalized Kreiss resolvent condition. Our…
On the classification of capillary graphs in Euclidean and non-Euclidean spaces
Giulio Colombo, Alberto Farina, Marco Magliaro +2
We prove some rigidity and classification results for graphs with prescribed mean curvature and locally constant Dirichlet and Neumann data, for instance as they appear in capillar…
One-dimensional symmetry results for semilinear equations and inequalities on half-spaces
Nicolas Beuvin, Alberto Farina
We prove new one-dimensional symmetry results for non-negative solutions, possibly unbounded, to the semilinear equation in the upper half-space .…
Monotonicity for solutions to semilinear problems in epigraphs
Nicolas Beuvin, Alberto Farina, Berardino Sciunzi
We consider positive solutions, possibly unbounded, to the semilinear equation on continuous epigraphs bounded from below. Under the homogeneous Dirichlet boundary condi…
Serrin's overdetermined problems on epigraphs
Nicolas Beuvin, Alberto Farina
In this work we establish some rigidity results for Serrin's overdetermined problem \begin{equation*} \left\{ \begin{array}{cll} - Δu=f(u) & \text{in}& Ω,\newline u > 0& \text{in}…