M. Squassina

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math.AP2025

Quantitative and exact concavity principles for parabolic and elliptic equations

Marco Gallo, Riccardo Moraschi, Marco Squassina

Goal of this paper is to study classes of Cauchy-Dirichlet problems which include parabolic equations of the type $u_{t} - Δ u = a (x, t) f (u) in Ω \times (0, T)$ with $Ω\subse…

math.AP2024

Power law convergence and concavity for the Logarithmic Schrödinger equation

Marco Gallo, Sunra Mosconi, Marco Squassina

We study concavity properties of positive solutions to the Logarithmic Schrödinger equation $- Δ u = u lo g u^{2}$ in a general convex domain with Dirichlet conditions. To this aim, we…

math.AP2024

Concavity and perturbed concavity for $p$ -Laplace equations

Marco Gallo, Marco Squassina

In this paper we study convexity properties for quasilinear Lane-Emden-Fowler equations of the type $$\begin{cases} -Δ_p u = a(x) u^q & \quad \hbox{ in $Ω$ },\\ u >0 & \quad \hbox{…

Quantitative and exact concavity principles for parabolic and elliptic equations

Power law convergence and concavity for the Logarithmic Schrödinger equation

Concavity and perturbed concavity for p-Laplace equations

Concavity and perturbed concavity for $p$ -Laplace equations