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…
Eventi
Introduzione agli omeomorfismi quasi-conformi – Kirill Kuzmin (Università di Pisa)
Gli omeomorfismi quasi-conformi sono definiti rilassando la condizione di conformalità con una disuguaglianza. Essi hanno trovato applicazione in numerose aree della Matematica. In questo seminario daremo una breve introduzione agli omeomorfismi…
A randomized version of the Littlewood Conjecture – Part II: discussion – Henna Koivusalo (University of Vienna)
The Littlewood Conjecture in Diophantine approximation can be thought of as a problem about covering the plane by a union of hyperbolas centered at rational points. In this paper we consider the problem of translating the center of each hyperbola by…
A randomized version of the Littlewood Conjecture – Part I – Henna Koivusalo (University of Vienna)
The Littlewood Conjecture in Diophantine approximation can be thought of as a problem about covering the plane by a union of hyperbolas centered at rational points. In this paper we consider the problem of translating the center of each hyperbola by…
Disuguaglianze alla Basmajian per rappresentazioni massimali – Beatrice Pozzetti (Warwick)
Le rappresentazioni massimali sono le famiglie di sottogruppi di Sp(2n,R) isomorfi al gruppo fondamentale di una superficie iperbolicache massimizzano l’invariante di Toledo, un’opportuna nozione di volumeadatta a questo contesto. Non solo formano…
Cohesive behaviour arising in homogenization of Mumford-Shah type functionals – Marco Barchiesi (Universita’ di Napoli Federico II)
I will discuss the effective properties of a composite material whose micro-structure is constituted by a brittle material with periodically distributed soft inclusions. In particular, I will show that the presence of the soft inclusions gives rise,…
A PDE approach to a 2-dimensional matching problem – Federico Stra (Scuola Normale Superiore Pisa)
We prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected quadratic transportation cost for empirical measures of two samples of independent uniform…
Flusso geodetico e gruppo fondamentale in curvatura negativa – Matthieu Gendulphe (Università di Pisa)
Dai lavori di Hadamard (1898) e Morse (1918) sappiamo che le geodetiche delle superfici con curvatura negativa non dipendono dalla metrica, ma soltanto dalla topologia. Lo scopo del seminario sarà quello di spiegare una generalizzazione di questo…
A variational model for chiral liquid crystals – Marcello Ponsiglione (Universita’ di Roma La Sapienza)
I will introduce a discrete variational model for chiral liquid crystals. The order parameter in this model is an angle measuring the orientation of the chiral molecules. The corresponding energy is a slight variant of the XY energy, which also…
Ground states of a two phase model with cross and self attractive interactions – Lucia De Luca (TU Muenchen )
We consider a variational model for two interacting species (or phases), subject to cross and self attractive interactions. We show existence and several qualitative properties of minimizers. Depending on the strengths of the attractive forces,…