Sala Seminari (Dip. Matematica)

Bodies of minimal aerodynamic resistance with a relaxed convexity constraint.

Relatore: 
Edoardo Mainini
Abstract. We characterize the solution to the Newton minimal resistance problem in a specific class of hollow profiles, satisfying a q-concavity condition. We treat two-dimensional bodies and radially symmetric three-dimensional bodies.
Data Seminario: 
Wednesday, March 22, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 18:00
Affiliazione: 
Universita' di Genova
Ora Inizio: 
0000 - 17:00

A quasilinear equation with orthotropic structure

Relatore: 
Lorenzo Brasco
Abstract. We present a variant of the $p-$Laplacian operator, which arises as the first variation of a suitable Dirichlet integral. The corresponding elliptic equation is much more degenerate and singular than that for the standard $p-$Laplacian operator and regularity of the gradient of solutions appears to be a difficult issue. We will show some regularity results (differentiability, boundedness and continuity).
Data Seminario: 
Wednesday, March 8, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 18:00
Affiliazione: 
Universita' di Ferrara
Ora Inizio: 
0000 - 17:00

Continuous family of conserved energies for NLS, KdV and mKdV

Relatore: 
Herbert Koch

In this talk based on joint work with Kienzler and Vazquez I will
explain how Caffarelli's strategy of proving regularity for free
boundary problems can be implemented for the porous medium equation.
Elements of the proof is  a global existence result for Lipschitz
perturbations of flat fronts of C. Kienzler following my strategy with
Tataru for the Navier-Stokes equations, a careful construction of
comparison solutions, and Gaussian estimates in a subelliptic setting

Data Seminario: 
Wednesday, February 15, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 18:00
Affiliazione: 
Bonn
Ora Inizio: 
0000 - 17:00

Torsion in negative curvature

Tipo Seminario: 
Relatore: 
Roman Sauer

A classical theorem of Gromov states that the Betti numbers, i.e. the size of the free part of the homology groups, of negatively curved manifolds are bounded by the volume. We extend this theorem to the torsion part of the homology in all dimensions d > 3. From Gromov’s work it is known that in dimension 3 the size of torsion homology cannot be bounded in terms of the volume. In dimension 4 we give a somewhat precise estimate for the number of negatively curved manifolds of finite volume, up to homotopy, and in dimension d > 4 up to homeomorphism.

Data Seminario: 
Tuesday, April 11, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 16:00
Affiliazione: 
Karlsruhe Institute of Technology
Ora Inizio: 
0000 - 15:00

Regularity of stable solutions of $p$-Laplace equations through geometric Sobolev type inequalities

Abstract. We prove a Sobolev and a Morrey type inequality involving the mean curvature and the tangential gradient with respect to the level sets of the function that appears in the inequalities. Then, as an application, we establish \textit{a priori} estimates for semistable solutions of $-\Delta_p u= g(u)$ in a smooth bounded domain $\Omega\subset \mathbb{R}^n$. In particular, we obtain new $L^r$ and $W^{1,r}$ bounds for the extremal solution $u^\star$ when the domain is strictly convex. More precisely, we prove that
Data Seminario: 
Wednesday, February 1, 2017
Relatore: 
Daniele Castorina
Ora Fine: 
0000 - 18:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
0000 - 17:00

How to "synthesize" sub-fixed point sets into the global one just by looking inside groups?

Tipo Seminario: 
Relatore: 
Masato Mimura

Consider a group G action on a metric space X by isometries, and subgroups M_1,..., M_l. One interesting and important problem is to study conditions under which non-emptyness of each M_i-fixed points ensures that of global (G-)fixed points. One extreme case is where G is a simple Lie group, X is an origin-excluded Hilbert space, and the action is given by a (strongly continuous) unitary representation. Then, the Howe--Moore property, based on the Mautner phenomenon,  implies that for each(!) non-compact closed subgroup M, the existence of M-fixed points suffices that of G-fixed points.

Data Seminario: 
Thursday, January 12, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 17:00
Affiliazione: 
Tohoku university e EPF Lausanne
Ora Inizio: 
0000 - 16:00

Seminario di Algebra e Geometria - "Spectral sequences in local cohomology"

Relatore: 
Santiago Zarzuela

Abstract. Spectral sequences are often applied to compute local cohomology functors.
In this talk I’m going to review their use in order to calculate local
cohomology from the primary decomposition of an ideal I in a commutative Noetherian ring R. By one hand,  we shall deal with the
 computation of several generalized local cohomology functors supported on I. On the other hand, we will be mainly concerned with
 the computation of the local cohomology of R/I.

Data Seminario: 
Monday, December 19, 2016
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 15:30
Affiliazione: 
Università di Barcellona
Ora Inizio: 
0000 - 14:30

A direct approach to an epiperimetric inequality for Free-Boundary problems

Abstract. Using a direct approach, we prove a 2-dimensional epiperimetric inequality for the one-phase problem in the scalar and vectorial cases and for the double-phase problem. From this we deduce the $C^{1,α}$ regularity of the free-boundary in the scalar one-phase and double-phase problems, and of the reduced free-boundary in the vectorial case, without any restriction on the sign of the component functions. In this talk I will try to explain the proof of the epiperimetric inequality in the scalar one-phase problem. This is joint work with Bozhidar Velichkov.
Data Seminario: 
Wednesday, January 11, 2017
Relatore: 
Luca Spolaor
Ora Fine: 
0000 - 18:30
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
0000 - 17:00

Up to a small error, all functions are s-harmonic

Abstract. We would like to present a series of structural results on nonlocal operators. First of all, we will show that "all functions are s-harmonic, up to a small error", namely that any smooth function can be locally approximated by functions whose fractional Laplacian vanishes. This phenomenon is indeed very general and robust, since related approximation results hold true for all linear nonlocal operators. In particular, no particular structure (such as ellipticity, parabolicity or hyperbolicity) is needed to obtain these density results.
Data Seminario: 
Thursday, January 19, 2017
Relatore: 
Serena Dipierro
Ora Fine: 
0000 - 18:30
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
0000 - 17:00

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