
Seminario di Calcolo delle
Variazioni & Equazioni alle Derivate Parziali

I seminari si tengono di norma di venerdì alle ore 14:30
nella Sala Conferenze "Franco Tricerri" del Dipartimento di
Matematica e Informatica "Ulisse Dini" (Viale Morgagni 67/A).
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A.A. 2019 / 2020
::: PROSSIMO SEMINARIO: :::
I seminari sono sospesi fino a quando non riprenderanno le attività del Dipartimento.
:: Seminari passati: ::
28 febbraio 14:30 
Andreas Bernig (GoetheUniversität Frankfurt)

A ChernGaussBonnet theorem for metrics with changing signature


Abstract:
The classical ChernGaussBonnet theorem gives a relation
between the geometry and the topology of a Riemannian manifold. More
precisely, the Euler characteristic is given as integral over some
polynomial expression in the curvature tensor. We generalize this
theorem to manifolds endowed with a generic symmetric $(0,2)$tensor
which may have changing signature. Examples of such manifolds are
Hessiantype metrics; they also appear in physics (general relativity,
cosmology, quantum gravity, optical metamaterials). Our main theorem
states that for such a manifold, the Euler characteristic is obtained by
integrating some natural distribution over the manifold. The proof is
based on a pseudoRiemannian version of the Weyl principle and uses
Alesker's theory of valuations on manifolds. This is joint work with
Dmitry Faifman, Univ. Montréal and Gil Solanes, UA Barcelona.
21 febbraio 14:30 e 15:30 
Frank Duzaar (FAU ErlangenNürnberg)

Integral convexity and parabolic systems
 Verena Bögelein (Universität Salzburg)

Hölder continuity for a homogenous doubly nonlinear equation


Abstract Duzaar
Abstract Bögelein
14 febbraio 14:30 
Giulio Ciraolo (Università di Milano)

Symmetry results for critical pLaplace equations


Abstract
24 gennaio 14:30 
Alberto Roncoroni (Università di Firenze)

Serrin's type rigidity results


Abstract: The talk deals with overdetermined elliptic boundary value problems for bounded domains in the Euclidean space and, more in general, in Riemannian manifolds. Starting from the wellknown Serrin's rigidity result, an analogue result for domains inside convex cones of the Euclidean space will be considered. This part is based on a joint work with G. Ciraolo and on a recent project in collaboration with G. Ciraolo, P. Sicbaldi and B. Sirakov.
Moreover, rigidity results and counterexamples in space forms (the hyperbolic space and the sphere) will be shown. In the context of more general Riemannian manifolds (such as model manifolds and warped product manifolds), several rigidity results for overdetermined problems will be considered. This part is based on a joint work with A. Farina.
17 gennaio 14:30, AULA 1 
Antonia Passarelli di Napoli (Università di Napoli Federico II)

Regolarità per minimi di una classe di funzionali con convessità degenere


10 gennaio 2020 14:30 e 15:30 
Toru Kan (Osaka Prefecture University)

A remark on the behavior of solutions of the AllenCahn equation in the whole plane
 Michiaki Onodera (Tokyo Institute of Technology)

Hyperbolic solutions to Bernoulli's free boundary problem


Abstract Toru Kan:
We are concerned with the behavior of the interface (level curve) of
solutions of the AllenCahn equation in the whole plane. It is known
that the interface of a radially symmetric solution moves slightly
slower than that of a planar traveling wave solution. More specifically,
the distance of the interfaces grows logarithmically as time goes to
infinity. In this talk, we show that the distance between the interface
of some solution and that of a planar traveling wave solution can grow
polynomially.
Abstract Michiaki Onodera:
Bernoulli's free boundary problem is an overdetermined problem in which
one seeks an annular domain such that the capacitary potential satisfies
an extra boundary condition.
There exist two different types of solutions called elliptic and
hyperbolic solutions.
Elliptic solutions are ``stable'' solutions and tractable by
variational methods and
maximum principles, while hyperbolic solutions are ``unstable''
solutions of which
the qualitative behavior is less known.
I will present a joint work with Antoine Henrot (Institute Elie
Cartan), in which we
introduce a new implicit function theorem based on parabolic maximal regularity,
applicable to problems with loss of derivatives.
Clarifying the spectral structure of the corresponding linearized operator by
harmonic analysis, we prove the existence of foliated hyperbolic
solutions as well as elliptic solutions in the same regularity class.
13 dicembre 14:30 e 15:30 
Lisa Beck (Augsburg University)

On the structure of BV minimizers of linear growth functionals
 Nikos Katzourakis (University of Reading)

On the existence and uniqueness of vectorial absolute minimisers in Calculus of Variations in Linfinity


Abstract Beck
Abstract Katzourakis:
Calculus of Variations in the space Linfinity has a
relatively short history in Analysis. The scalarvalued theory was
pioneered by the Swedish mathematician Gunnar Aronsson in the 1960s and
since then has developed enormously. The general vectorvalued case
delayed a lot to be developed and its systematic development began in
the 2010s. One of the most fundamental problems in the area which was
completely open until today (and has been attempted by many researchers)
concerned that of the title. In this talk I will discuss the first
result in this direction.
6 dicembre 14:30, AULA 7 
Nicola Garofalo (Università di Padova)

Sobolev and isoperimetric inequalities for KolmogorovFokkerPlanck operators


Abstract: In his seminal 1934 paper on Brownian motion and the theory of gases Kolmogorov introduced a second order hypoellipitc evolution equation which displays many challenging features. Thirty years later, in the opening of his famous 1967 hypoellipticity paper, Hormander discussed a general class of degenerate OrnsteinUhlenbeck operators that includes Kolmogorov's as a special case. The natural semigroups attached to such equations need not be symmetric or doubling, thus the existing theories do not readily apply. As a consequence, despite the large amount of work done by many people over the past thirty years, some basic questions have remained unsettled, such as HardyLittlewoodSobolev and Isoperimetric inequalities and the study of local and nonlocal minimal surfaces. In this lecture I will present some interesting developments in the above program. This is joint work with Giulio Tralli.
22 novembre 11:0017:30, a Pisa 
MathAnalysis@UniFIPISI 
Incontri di Analisi Matematica tra Firenze, Pisa e Siena 

Organizzato da G. Bellettini, F. Bucci, E. Chiodaroli, A. Colesanti, E. Paolini, N. Visciglia.
La registrazione, il programma dettagliato ed ulteriori informazioni si trovano
qui
15 novembre 14:30 
Richard J. Gardner (Western Washington University)

The Minkowski Problem


Abstract
8 novembre 14:30 
Vít Musil (Università degli Studi di Firenze e Czech Academy of Sciences)

Moser inequalities in Gauss space


Abstract
25 ottobre 14:30 e 15:30, AULA 7 
Virginia Agostiniani (Università di Verona)

Symmetries for the torsion problem in a multiply connected domain
 Luca Nenna (Université Paris SudOrsay)

Grand Canonical Optimal Transport


Abstract Agostiniani: In this talk, we discuss some recent symmetry results for the torsion problem, when the domain considered has multiple boundary components. This is a joint project with S. Borghini and L. Mazzieri.
Abstract Nenna: In this talk I will firstly review standard multimarginal
Optimal Transport (where a number N of marginals is fixed) focusing, in
particular, on the applications in Quantum Mechanics (in this case the
marginals are all the same and represent the electrons of an atom or a
molecule). I will then extend the Optimal Transportation problem to the
grand canonical setting: only an average number of marginals is now
given (i.e. we can now define a OT problem with a fractional number of
marginals), discussing existence, duality and numerical methods. I will
finally compare these two problems and show how they behave differently
despite considering the same cost functions. This a joint work with S.
Di Marino and M. Lewin.
4 ottobre 14:30 
Adolfo Arroyo Rabasa (University of Warwick)

Geometric rigidity of tangent symmetric gradient measures


Abstract
23 settembre 2019 14:30 e 15:30 
Gamze Duzgun (Hacettepe University Ankara)

Existence of Three Nontrivial Solutions for a Nonlinear Fractional
Laplacian Problem
 Hacer Ilhan (Hacettepe University Ankara)

Similarity Searches in Motion Capture Databases


Organizzatori: Chiara Bianchini, Giuliano Lazzaroni.
Seminari dell'a.a. 2018/19
Seminari dell'a.a. 2017/18
Seminari dell'a.a. 2016/17
Seminari dell'a.a. 2015/16
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Seminari dell'a.a. 2013/14
Seminari dell'a.a. 2011/12
Seminari dell'a.a. 2010/11
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Seminari dell'a.a. 2008/09
Seminari dell'a.a. 2007/08
Seminari dell'a.a. 2006/07