Abstract: The problem of an elastic rod deforming in a plane, namely the so-called ‘planar elastica’, has a long history, rooting to Jacob Bernoulli (1654-1705), Daniel Bernoulli (1700-1782), Leonhard...
Abstract: Graphene, a carbon layer packed in a 2D honeycomb lattice, has been discussed theoretically in the 1940s, tough it took sixty years to be experimentally isolate...
Abstract: The unique electronic properties of graphene have attracted a huge amount of attention since its discovery in 2004. The structural properties of such a two-dimensional lattice are less known...
We discuss vortex configurations in the abelian self-dual Chern-Simons-Higgs model, where topological invariants can just describe a part of the picture. We construct non-topological condensates (=dou...
Building upon the Almgren's big regularity paper, Chang proved in the eighties that the singularities of area-minimizing integral 2-dimensional currents are isolated. His proof relies on a suitable im...
The asymptotic decay rate and other qualitative features of solutions to parabolic equations set in noncompact domains of RN, or Riemannian manifolds, depend in general on a suitable notion of the geo...
We discuss some recent results related to the homogeneous Dirichlet problem for the infinity Laplace equation with constant source in a bounded domain. We characterize the geometry of domains for whic...
We consider vectorial variational problems of the form E[u]=∫W(Du)dx, typical for example of nonlinear elasticity and plasticity, which include constraints on the determinant. Specifically, the ener...
Segregation phenomena occurs in many areas of mathematics and science: from equipartition problems in geometry, to social and biological processes (cells, bacteria, ants, mammals) to finance (sellers ...
The well-studied power-law-nonlinearity elliptic PDE is known to exhibit a variety of interesting effects, including non-existence, non-uniqueness and concentration phenomena. The application of forma...
In the 80s, De Giorgi introduced the notion of abstract gradient flows, which allowed to define a notion of solutions to ordinary differential equations of the form x' = −grad F(x) on metric spaces ...
