arXiv subjects

Andrea Dall'Aglio

Publications and source records attributed to Andrea Dall'Aglio.

4 recordsLinked to original sources

arXiv2025

Quasi-linear parabolic equations having a superlinear gradient term which depends on the solution

In this paper, we study existence and regularity for solutions to parabolic equations having a superlinear lower order term depending on both the solution and its gradient. Two different situations are analyzed. On the one hand, we assume that the initial datum belongs to an Orlicz space of exponentially summable functions. On the other, data in an appropriate Lebesgue space satisfying a smallness condition are considered. Our results are coherent with those of previous papers in similar frameworks.

math.AP↗

arXiv2017

The Shapley Value in the Knaster Gain Game

In Briata, Dall'Aglio and Fragnelli (2012), the authors introduce a cooperative game with transferable utility for allocating the gain of a collusion among completely risk-averse agents involved in the fair division procedure introduced by Knaster (1946). In this paper we analyze the Shapley value (Shapley, 1953) of the game and propose its use as a measure of the players' attitude towards collusion. Furthermore, we relate the sign of the Shapley value with the ranking order of the players' evaluation, and show that some players in a given ranking will always deter collusion. Finally, we characterize the coalitions that maximize the gain from collusion, and suggest an ad-hoc coalition formation mechanism.

math.OC↗

arXiv2015

Existence of solutions for degenerate parabolic equations with singular terms

In this paper we deal with parabolic problems whose simplest model is $$ \begin{cases} u'- Δ_{p} u + B\frac{|\nabla u|^p}{u} = 0 & \text{in} (0,T) \times Ω,\newline u(0,x)= u_0 (x) &\text{in}\ Ω, \newline u(t,x)=0 &\text{on}\ (0,T) \times \partialΩ, \end{cases} $$ where $T>0$, $N\geq 2$, $p>1$, $B > 0$, and $u_{0}$ is a positive function in $L^{\infty}(Ω)$ bounded away from zero.

math.AP↗

arXiv2012

Local and global regularity of weak solutions of elliptic equations with superquadratic Hamiltonian

In this paper, we study the regularity of weak solutions and subsolutions of second-order elliptic equations having a gradient term with superquadratic growth. We show that, under appropriate integrability conditions on the data, all weak subsolutions in a bounded and regular open set $\Om$ are Hölder-continuous up to the boundary of $\Om$. Some local and global summability results are also presented. The main feature of this kind of problems is that the gradient term, not the principal part of the operator, is responsible for the regularity.

math.AP↗