[CvGmt News] CVGMT: weekly bulletin

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Fri Sep 27 12:00:02 CEST 2013

Subject: CVGMT weekly bulletin

Weekly bulletin of http://cvgmt.sns.it/

--- Summary ---

* Seminars by: BogachevVittoneSpadaroMonti
* New papers by: Savar?, Rossi, Dipierro, Julin, Mielke, Paolini, Valdinoci, Palatucci, Fusco
* Modified papers by: Vittone, Buttazzo, Freddi, Treu, Pinamonti, Donadello, Spadaro, Eleuteri, Roubicek, Rossi, Lussardi, Knees, Zanini, Mielke, Segatti, Crippa, De Lellis, Scardia, Stefanelli, Bucur, Spinolo, Zeppieri, Fiaschi, Solombrino, M?ller, Serra Cassano

--- Seminars next week ---

* Monday 30 sep 2013

Centro De Giorgi

Sobolev classes over infinite-dimensional spaces with measures
Vladimir Bogachev 
ERC-School on Geometric Measure Theory and Real Analysis

Abstract. This mini-course aims at giving a concise introduction to the theory of Sobolev classes over infinite-dimensional spaces with measures. The framework is a natural generalization of the finite-dimensional case of weighted Sobolev classes with sufficiently differentiable (or even smooth) weights. To this end, suitable classes of differentiable measures will be introduced. The associated Sobolev classes are defined by means of completions in Sobolev norms or via integration by parts formulae. The Gaussian case will be also considered. Basic results will be presented and challenging open problems will be mentioned. 

Centro De Giorgi

The regularity problem for sub-Riemannian geodesics
Davide Vittone (Dip. Matematica, Univ. di Padova)
ERC-School on Geometric Measure Theory and Real Analysis

Abstract. We study the regularity problem for sub-Riemannian geodesics, i.e., those curves that minimize length among all curves joining two fixed endpoints and whose derivatives are tangent to a given, smooth distribution of planes with constant dimension. We will review necessary conditions for optimality, focusing in particular on Pontryagin Maximum Principle and Goh condition. The regularity problem is non-trivial due to the presence of the so-called abnormal extremals, i.e., certain curves satisfying the necessary conditions that may develop singularities. After reviewing the recent literature on the subject, we will focus on the case of stratified groups and present some recent results obtained in collaboration with E. Le Donne, G. P. Leonardi and R. Monti. 

Centro De Giorgi

Regularity of higher codimension area minimizing integral currents
Emanuele Spadaro 
ERC-School on Geometric Measure Theory and Real Analysis

Abstract. In this series of lectures I will present a new proof of the partial regularity for area minimizing integral currents in any dimension and codimension (obtained in collaboration with C. De Lellis at Zurich), as proven first in Almgren's big regularity paper. After a brief introduction to currents and multiple valued functions, I will focus on the core of the partial regularity results, trying to give a fairly detailed description of the approximation of a current on a center manifold and of the frequency function estimates. 

Centro De Giorgi

Isoperimetric problem and minimal surfaces in the Heisenberg group
Roberto Monti (Universit? di Padova)
ERC-School on Geometric Measure Theory and Real Analysis

Abstract. The lecture is an introduction to Geometric Measure Theory, H-perimeter, minimal surfaces, and to the isoperimetric problem in the Heisenberg group. 
1. Introduction. The Heisenberg group and its Lie algebra, Carnot-Caratheodory metric, functional spaces and inequalities. 
2. H-perimeter. Sets with finite H-perimeter, blow-up and structure theorems, different notions of surface area, area formulas. 
3. Isoperimetric problem. Existence of isoperimetric sets, Pansu conjecture, convex, C^2, and symmetric solutions, rearrangements. 
4. H-minimal surfaces. Minimal surfaces equations, nonregular minimal surfaces, approximation of minimal boundaries, the regularity problem. 

--- New Papers ---

* Paolini: Minimal connections: the classical Steiner problem and generalizations

* Dipierro, Palatucci, Valdinoci: Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting

* Mielke, Rossi, Savar?: Balanced Viscosity (BV) solutions to infinite-dimensional rate-independent systems

* Fusco, Julin: On the regularity of critical and minimal sets of a free interface problem

--- Modified Papers ---

* Bucur, Buttazzo, Stefanelli: Shape flows for spectral optimization problems

* Fiaschi, Knees, Stefanelli: Young-measure quasi-static damage evolution

* Stefanelli: The De Giorgi conjecture on elliptic regularization

* Rossi, Segatti, Stefanelli: Global attractors for gradient flows in metric spaces

* Mielke, Stefanelli: Weighted energy-dissipation functionals for gradient flows

* Mielke, Stefanelli: Linearized plasticity is the evolutionary Gamma-limit of finite plasticity

* Eleuteri, Lussardi, Stefanelli: Thermal control of the Souza-Auricchio model for shape memory alloys

* Solombrino: Quasistatic evolution in perfect plasticity for general heterogeneous materials.

* Freddi, Roubicek, Zanini: Quasistatic delamination of sandwich-like Kirchhoff-Love plates

* M?ller, Scardia, Zeppieri: Geometric rigidity for incompatible fields and an application to strain-gradient plasticity

* Pinamonti, Serra Cassano, Treu, Vittone: BV Minimizers of the area functional in the Heisenberg group under the bounded slope condition

* Crippa, Donadello, Spinolo: Initial-boundary value problems for continuity equations with $BV$ coefficients

* Crippa, Donadello, Spinolo: A note on the initial-boundary value problem for continuity equations with rough coefficients

* De Lellis, Spadaro: Regularity of area-minimizing currents III: blow up

* De Lellis, Spadaro: Regularity of area-minimizing currents II: center manifold

* De Lellis, Spadaro: Regularity of area-minimizing currents I: $L^p$ gradient estimates

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