Seminari e convegni

Descrizione

Pasquale Ambrosio (University of Naples “Federico II”)

“Regularity results for a class of strongly degenerateparabolic equations”

Motivated by applications to gas filtration problems, we study the

regularity of weak solutions to the strongly degenerateparabolic PDE

ut – div [((|Du| – 𝜈)+)^{p-1}Du/|Du|] = f in ΩT = Ω × (0, T),

where Ω is a bounded domain in Rn for n ≥ 2, p ≥ 2, 𝜈 is a positive

constant and (⋅)+ stands for the positive part. Assumingthat the datum

f belongs to a suitable Lebesgue-Sobolev parabolic space, weestablish

the Sobolev spatial regularity of a nonlinear function ofthe spatial

gradient Du of the weak solutions, which in turn implies theexistence

of the weak time derivative ut. Next, we weaken theassumption on the

right-hand side, by assuming that f belongs to a suitablelocal

Lebesgue-Besov space. This leads us to obtain fractionalSobolev

regularity results for a function of Du, which in turn yieldthe higher

summability of Du with respect to the spatial variable. Themain novelty

here is that the structure function of the above equationsatisfies

standard growth and ellipticity conditions only outside theball with

radius 𝜈 centered at the origin.

This is a joint research with Antonia Passarelli di Napoli(University

of Naples “Federico II”).

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Emanuele Cristoforoni (SSM)

Titolo: A thermal insulation problem witha prescribed heat source

Abstract: We study the thermal insulationof a bounded body $Omegasubsetmathbb{R}^n$, under a prescribed heat source$f > 0$, via a bulk layer of insulating material. We consider a model ofheat transfer between the insulated body and the environment determined byconvection; this corresponds to Robin boundary conditions on the free boundaryof the layer. We show that a minimal con guration exists and that it satisfiesuniform density estimates.

Descrizione
Martin Mayer, Scuola Superiore Meridionale, Naples, Italy

“The prescribed scalar curvature problem in the negative Yamabe case ”

We will discuss some recent progress
on the conformally prescribed scalar curvature problem
in case of a negative Yamabe invariant,
which is resolved,
if the function K to be prescribed is strictly negative,
while necessary and sufficient conditions are known,
if K is nowhere positive.
On the other hand, if K is sign changing,
little is known in general beyond smallness assumptions
on the max(K,0). We adress the latter case variationally,
still in the realm of smallness assumptions,
and shed some light on the underlying features of the problem.
The presented techniques do not only allow to recover,
what is known up to now, in a quite natural way,
but also adds some new existence results.
Time permitting, we shall exemplify, what happens,
if the smallness assumptions fail.
In collaboration with Chaona Zhu, University Tor Vergata, Rome, Italy.

Descrizione

Alba Lia Masiello (UniNa)

“Estimates for Robin p-Laplacian eigenvalues of convex sets with prescribed perimeter”

We will consider the shape optimization problem of minimizing/maximizing

the first eigenvalue of the p-Laplace operator with Robin boundary

conditions in the class of convex sets. In particular, when imposing a

perimeter constraint, we will study the behavior of the eigenvalues as

the boundary parameter beta varies in R. We prove an upper bound for the

first Robin eigenvalue of the p-Laplacian with a positive boundary parameter and a quantitative

versionof the reverse Faber-Krahn type inequality for the first Robin eigenvalue of the

p-Laplacian with negative boundary parameter, making use of a comparison

argument obtained by means of inner parallel sets.

The results are contained in a joint work with V. Amato and A. Gentile.

Vincenzo Amato (UniNa)

“Somea symptotic quantitative inequalities”.

Abstract:The classical quantitative isoperimetric inequality has opened the way for a rich line of research into quantitative versions of many inequalities. In practice, such an inequality aims to estimate how much a set with an almost minimal perimeter must be ‘similar’ to a ball.

We will discuss the case where a spectral inequality is not achieved. In particular, we will analyse the case of two inequalities, one concerning torsional rigidity and the other the first non-trivial Neumann eigenvalue, both of which are asymptotically achieved by a sequence of thinning rectangles.

Joint works with D. Bucur, A.L. Masiello, G. Paoli and R. Sannipoli.

I will try to describe some of the thingswe have learnt, over the past few years, about three fundamental questions inthe global theory of free boundary minimal surfaces; given that context, I willthen focus on one of the latest advances, that is a methodology to gaineffective estimates on the spectrum of Schrödinger-type operators by designingsuitable partitions of the domain and associated collections of mixed boundaryvalue problems. As an application, this allowed us to obtain the firsttwo-sided, explicit affine bounds on the Morse index of various families ofFBMS in the three-dimensional Euclidean ball. The lecture is aimed at thegeneral mathematical audience.

Il giorno Martedì 17 Ottobre 2023 alle ore 14,30 nella Sala Professori al I Livello del DMA,  il Dott. Stefano Buccheri dell’Università di Vienna terrà il seguente seminario:

Titolo: ‘Viscosity solutions for nonlocal equations with space-dependent operators’.

Abstract: This talk focuses on a nonlocal operator of fractional-laplacian type, where integration is taken on a variable domain. Similar operators arise naturally in the hydrodynamic limit of suitable kinetic equations in bounded domains.
We prove that the associated elliptic and parabolic problems admit a unique viscosity solution. In addition, we study the corresponding eigenvalue problems. This is a joint work with Ulisse Stefanelli.

Fernando Farroni e Gabriella Zecca

il giorno 25 Ottobre 2023 alle ore 14:30

Anna Vidotto
Dipartimento di Matematica e Applicazioni
Università degli studi di Napoli FEDERICO II

terrà un seminario

dal Titolo: The Malliavin-Stein Approach and an Improved Second-Order Poincaré Inequality.

Abstract: In this talk we will introduce the so-called Malliavin-Stein approach for obtaining quantitative central limit theorems for functionals of Gaussian fields, that this combination works admirably well was discovered by Nourdin and Peccati in their seminal paper from 2009. Then we will present an improved version of the second-order Gaussian Poincaré inequality, first introduced in Chatterjee (2009) and Nourdin et al. (2009), and consequent applications.

Il seminario si terrà nella Sala Professori Primo livello al Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli FEDERICO II,  Complesso di Monte Sant’Angelo, Via Cintia, Napoli.

Sarà anche possibile seguirlo online mediante Teams al seguente link:

https://teams.microsoft.com/l/meetup-join/19%3aMQ4RZDBo_0G-K_PHxKtktVYAczOGbTqLmWu95Avgs0s1%40thread.tacv2/1697451725484?context=%7b%22Tid%22%3a%222fcfe26a-bb62-46b0-b1e3-28f9da0c45fd%22%2c%22Oid%22%3a%229413faf6-db8e-4858-98b1-442e3ee2a5df%22%7d

Enrica Pirozzi

Avviso di Seminario di Geometria e Algebra

dott.ssa Annamaria Iezzi

mercoledì 25 ottobre dalle 15:30 alle 16:30 in Aula C