Nonlinear PDEs: from geometry to population dynamics
| Componente | Categoria |
|---|---|
| Giulio Galise | Componenti strutturati del gruppo di ricerca |
| Filomena Pacella | Componenti strutturati del gruppo di ricerca |
| Luca Rossi | Componenti strutturati del gruppo di ricerca |
| Danilo Gregorin Afonso | Dottorando/Assegnista/Specializzando componente non strutturato del gruppo di ricerca |
| Fabiana Leoni | Componenti strutturati del gruppo di ricerca |
| Isabella Birindelli | Componenti strutturati del gruppo di ricerca |
| David Stolnicki | Dottorando/Assegnista/Specializzando componente non strutturato del gruppo di ricerca |
The research project focuses on PDE's arising, in particular, from problems in geometry or applied sciences. More precisely we will consider elliptic equations, both semilinear or fully nonlinear, and reaction-diffusion equations.
In the framework of elliptic equations arising in geometry we will study:
- overdetermined problems to the aim of characterizing the domains for which a solution exists;
- the question of prescribing Gaussian curvature under conformal changes of metrics admitting conical singularities and other PDE's admitting a variational formulation and involving exponential nonlinearities;
-scale invariant problems and critical exponents for Pucci's operators.
Concerning PDE's relevant in population dynamics and other applied sciences we plan to study:
- reaction-diffusion equations;
- definition and properties of the principle eigenvalues and eigenfunctions and related issues for fully nonlinear elliptic equations, with singular or degenerate principal part, associated with mixed boundary conditions, for "truncated-laplacians" and for operators given by a fractional laplacian plus a transport term.