I will discuss some contributions of Henri Poincaré which have had a major impact on the development of PDEs in the 20th century; in particular, the solution of the Laplace equation, the spectral theo...
A partire dalla sua introduzione alla fine degli anni '60 ad opera di Morawetz, il metodo del moltiplicatore è stato largamente e floridamente usato per ottenere vari importanti risultati nell'ambito ...
What is the analogue of the principal eigenvalue for elliptic operators with non-compact resolvents? Focusing on the case where the lack of compactness is due to the unboundedness of the domain, we sh...
We consider various examples of critical nonlinear partial differential equations which have the following common features: they are Hamiltonian, of dispersive nature, have a conservation law invarian...
Abstract: The mechanical behaviour of granular materials depends on their grading. Crushing of particles under compression or shear modifies the grain size distribution, with a tendency for the percen...
Abstract: According to Hund (1927) quantum mechanics forbids the existence of stable optically active (chiral) molecules as they violate the invariance under parity of the Hamiltonian. This paradox ha...
Abstract: Chiral surfaces, obtained through self-assembling of chiral molecules on achiral metallic surfaces, represent a relevant subject for technologically important issues in many fields, like sur...
Abstract: It has been known for centuries that a body in contact with a substrate will start to slide only when the lateral force exceeds the static friction force. The transition from static to dynam...
Abstract: The conversion of sunlight into electricity by photovoltaic materials is one of most attractive ways to satisfy the increasing demand of clean and sustainable energy. Nanoscience is strongly...
Abstract: We will discuss the mechanical bases of cellular motility by swimming and crawling.The photo, courtesy of A. Beran (OGS, Trieste), shows some Euglenids exhibiting "metaboly", a type of motio...
Abstract: Engineering design of robots is often inspired by nature; recently developed bioinspired robots accurately imitate various aspects of their live counterparts. Yet, the relationship between e...
We establish trace Hardy and trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants, for domains satisfying suitable geometric assumptions such as mean convexity or convexity. We then use t...
