6 citations · 13 across the 10 of their papers we have counts for
18 papers · 1 filter
The fractional Makai-Hayman inequality
Francesca Bianchi, Lorenzo Brasco
We prove that the first eigenvalue of the fractional Dirichlet-Laplacian of order on a simply connected set of the plane can be bounded from below in terms of its inradius only…
Convex duality for principal frequencies
Lorenzo Brasco
We consider the sharp Sobolev-Poincaré constant for the embedding of into . We show that such a constant exhibits an unexpected dual variational formulation,…
Gradient estimates for an orthotropic nonlinear diffusion equation
Pierre Bousquet, Lorenzo Brasco, Chiara Leone +1
We consider a quasilinear degenerate parabolic equation driven by the orthotropic Laplacian. We prove that local weak solutions are locally Lipschitz continuous in the spatial…
Long-time behavior for the porous medium equation with small initial energy
Lorenzo Brasco, Bruno Volzone
We study the long-time behavior for the solution of the Porous Medium Equation in an open bounded connected set, with smooth boundary. Homogeneous Dirichlet boundary conditions are…
Positive solutions to the sublinear Lane-Emden equation are isolated
Lorenzo Brasco, Guido De Philippis, Giovanni Franzina
We prove that on a smooth bounded set, the positive least energy solution of the Lane-Emden equation with sublinear power is isolated. As a corollary, we obtain that the first …
Continuity of solutions to a nonlinear fractional diffusion equation
Lorenzo Brasco, Erik Lindgren, Martin Strömqvist
We study a parabolic equation for the fractional Laplacian of order , for and . We provide space-time Hölder estimates for weak solutions, with explicit expo…