NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS ARISING IN GEOMETRY AND APPLIED SCIENCES
| Componente | Categoria |
|---|---|
| Andrea Davini | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Antonio Siconolfi | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Corrado Mascia | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Francesca De Marchis | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Marco Pozza | Dottorando/Assegnista/Specializzando componente non strutturato del gruppo di ricerca / PhD/Assegnista/Specializzando member non structured of the research group |
| Flavia Lanzara | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Isabella Birindelli | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Andrea Terracina | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Giulio Galise | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Fabiana Leoni | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
The research project focuses on some nonlinear PDE¿s arising, in particular, from problems in Geometry or Applied Sciences. More precisely we will consider elliptic equations, both semilinear or fully nonlinear, Hamilton-Jacobi equations and nonlinear conservation laws.
In the framework of elliptic equations 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
- fully nonlinear elliptic equations which involve degenerate, singular or uniformly elliptic operators.
Concerning Hamilton-Jacobi equations we plan to study :
- ergodic problems in noncompact settings
- discontinuous viscosity solutions on graphs and networks
- Hamilton Jacobi equations with discountinuous initial data
As far as conservation laws are concerned, we will study :
- measure valued solutions for scalar conservation laws
- propagating fronts for hyperbolic reaction-diffusion equations