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Seminars 2005-2006

Selezionare soluzioni deboli di una legge di conservazione scalare: una condizione minimale di entropia per flussi strettamente convessi

Green function for Boltzmann equation and applications

A weak Maximum Principle in Optimal Control

H1/2-maps with values into the circle, minimal connections and relaxation results

Malliavin Calculus of Bismut type without probability and its applications

The cyclical monotonicity in the mass transport problem and its sufficiency

A perturbative approach to material instabilities

Epsilon-stability: a new method for producing local minimizers in quasi-static fracture, and for some examples of Gamma Convergence

Existence and nonexistence of solutions for a system of elliptic equations of Schrödinger-Maxwell type

Gene network inference from gene expression time series

Confining thin elastic sheets and folding paper

Bang-bang and singular control problems: Applications, sufficient conditions and sensitivity analysis

The boundary Riemann solver coming from the real vanishing viscosity approximation

DNA Topology

Regularity and compactness for the flow associated to weakly differentiable vector fields

Coverings of Control Systems

Regularity of minima of multiple integrals

Dynamics in classical mean-field models for Ostwald Ripening

An estimate for the entropy of Hamiltonian flows

Variational models for domanin branching in materials

On the energetics of biomembranes and liposomes

Path functionals over Wassersein spaces

A general class of functionals which measure the cost of a path in a metric space joining two given points is considered and abstract existence results for optimal paths are provided. The results are then applied to the case the metric space is a Wasserstein space of probabilities on a given subset of the Euclidean space and the cost of a path depends on the value of classical functionals over measures, providing a model of mass transportation different from the classical Monge-Kantorovich theory.

Regularity criteria for weak solutions to Navier-Stokes equations

Recent progress on Camassa-Holm equation

Time optimal trajectories for a spin 1/2 particle ina magnetic field

A multiscale approach to the Neumann Sieve Problem in dimensional reduction

Convergent schemes for the Hunter-Saxton equation

The Hunter-Saxton equation is a nonlinear partial differentialequation that has been used as a simple model for liquid crystals. Itcan be written as$(u_t+u u_x)_x=\frac12 (u_x)^2$. We study various finite differenceapproximations to this equations, and show that they converge to asolution of the equation. This is joint work with K. H. Karlsen andN.H. Risebro, both from University of Oslo.

Regularity of Minimizers and of Adjoint States in OptimalControl under State Constraints

This talk is devoted to regularity of minimizers and adjoint statesfor the Bolza optimal control problem under state constraints. It iswell known that the adjoint state of the Pontryagin maximumprinciple may be discontinuous whenever the optimal trajectory lies partiallyon the boundary of constraints. Still we prove that if the associatedHamiltonian H(t,x,.) is differentiable and the constraints are sleek,then every optimal trajectory is continuously differentiable.Moreover if for all x on the boundary of constraints, the partial derivativeof H with respect to the last variable, H_p(t,x, .) iis strictlymonotone in directions normal at x to the set of constraints, thenthe adjoint state is also continuous on interior of its interval ofdefinition. Finally, we identify a class of constraints for which theadjoint state is absolutely continuous or even Lipschitz on this openinterval. This allows us to derive necessary conditions foroptimality in the form of variational differential inequalities, maximumprinciple and modified transversality conditions. We also providesufficient conditions for Lipschitz continuity of optimal controlsand for normality of the maximum principle.

On the geometry of configuration spaces of planarpolygons and mechanical linkages

It will be shown that, given a planar polygon ormechanical linkage, considerable geometric informationon the variety of its configurations can be obtainedusing the algebraic formulae for topologicalinvariants of quadratic mappings. As an illustration,the complete list of possible topological types ofplanar pentagons will be obtained. Similar resultswill be presented for spatial quadrangles and certainmechanical linkages. An application to investigationof the stereoisomery phenomenon for certain organicmolecules will be also outlined.

Time averaged optimization: singularities and bifurcations

Nonlinear capacity and applications to some nonlinearproblems

Last modified: 17 December 2006

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