Programme

Among the various topics to be covered at the conference, the main ones include the following:

• Variational Methods
  Variational methods are a fundamental mathematical framework for modeling, analyzing, and optimizing phenomena across physics and other applied sciences. By minimizing energy functionals, they lead to elliptic partial differential equations that describe equilibrium states and critical configurations. Their applications span diverse areas, including: stationary-wave solutions in Schrödinger-type equations, monochromatic electromagnetic waves governed by Maxwell’s equations, nonlinear diffusion in porous media (p-Laplace equation), minimal surfaces and interface geometry, and phase transitions (Allen–Cahn/Ginzburg–Landau equations).

• Bifurcation Theory
  A challenging approach to studying the existence of solutions is given by the so-called bifurcation theory. Originating in the works of Henri Poincaré and later formalized through contributions by mathematicians such as Krasnoselskii and Rabinowitz in the 20th century, bifurcation theory has become a fundamental tool in nonlinear analysis. In particular, bifurcation phenomena play a crucial role in the study of nonlinear elliptic problems, revealing how solution branches emerge and evolve in dependence on certain parameters. This approach not only deepens our understanding of the structure of solution sets but also provides insights into the qualitative behavior of complex systems. The conference will be focused on recent advances in this field, with contributions on both theoretical developments and applications to physical models.

• Regularity and Qualitative Properties
  One of the main challenges in understanding nonlinear phenomena driven by PDEs is to study the qualitative properties of their solutions, starting with regularity. Recently, attention has been turned to nonlinear elliptic PDEs, including of degenerate type. A key model problem is driven by the p-Laplace equation (scalar or vectorial). While important breakthroughs by eminent mathematicians such as Morrey, De Giorgi, Di Benedetto, etc. established a comprehensive regularity theory, the field continues to develop rapidly. These developments are the starting point for the study of symmetry and monotonicity properties, which can lead to uniqueness or non-existence results, as well as classification theorems.