Parabolic equations relative to vector fields.
Perron's method and the method of relaxed limits for "unbounded" PDE in Hilbert spaces
We prove that Perron's method and the method of half-relaxed limits of Barles-Perthame works for the so called B-continuous viscosity solutions of a large class of fully nonlinear unbounded partial differential equations in Hilbert spaces. Perron's method extends the existence of B-continuous viscosity solutions to many new equations that are not of Bellman type. The method of half-relaxed limits allows limiting operations with viscosity solutions without any a priori estimates. Possible applications...
Piecewise viscosity solutions for stochastic singular control.
Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies
Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death...
Problemi di ottimizzazione nella teoria delle code
Prolongement des jeux à deux joueurs de somme nulle. Une théorie abstraite des duels
Propagazione dei massimi e unicità di soluzioni di viscosità di equazioni completamente non lineari del primo e del secondo ordine