18 citations · 19 across the 3 of their papers we have counts for
3 papers
math.FA2016★ 18 cited
On the Moser-Trudinger inequality in fractional Sobolev-Slobodeckij spaces
Enea Parini, Bernhard Ruf
We consider the problem of finding the optimal exponent in the Moser-Trudinger inequality \[ \sup \left\{\int_Ω\exp{\left(α\,|u|^{\frac{N}{N-s}}\right)}\,\bigg|\,u \in \widetilde{W…
math.OC2015★ 1 cited
Reverse Cheeger inequality for planar convex sets
Enea Parini
We prove the sharp inequality \[ J(Ω) := \frac{λ_1(Ω)}{h_1(Ω)^2} < \frac{π^2}{4},\] where is any planar, convex set, is the first eigenvalue of the Laplacian under Dir…
math.AP2014
On the existence threshold for positive solutions of p-laplacian equations with a concave-convex nonlinearity
Fernando Charro, Enea Parini
We study the following boundary value problem with a concave-convex nonlinearity: \begin{equation*} \left\{ \begin{array}{r c l l} -Δ_p u & = & Λ\,u^{q-1}+ u^{r-1} & \textrm{in }Ω,…