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In this lecture I will consider the nonlinear elliptic model problem −div(A(x)∇u(x)) + cu(x) = γ...

Data assimilation problems consist in retrieving the value of the solution at some time (everywhere in the domain) for an evolution problem knowing informations on the solution on a subdomain during a...

Several transport-dffusion systems arise as simple models in chemotaxis (motion of bacterias or amebia interacting through a chemical signal) and in angiogenesis (development of capillary blood vessel...

Si studia il problema di Dirichlet per l’equazione della curvatura media sul disco con dato al bordo gamma. Il problema è variazionale e caratterizzato da mancanza di compattezza. Se la curvatura medi...

I will begin by giving a survey of some known methods for a-priori bounds of positive solutions of semilinear elliptic equations on smooth bounded domains with zero Dirichlet boundary conditions. I wi...

Si considera il problema di rimuovere una fissata quantita di materiale da una regione D nella maniera piu efficiente possibile. Per tener conto del fatto che non tutte le direzioni si percorrono con ...

I will discuss various modes of degeneration of differential operators and associated Lie algebras of vector fields and indicate a systematic approach to uniform invertibility under appropriate ellipt...

I will consider the quintic two-dimensional focusing nonlinear Schrodinger equation iut + ∆u +...

Lo studio dell’equazione iconale complessa e motivato dall’interesse per i cosiddetti raggi evanescenti, che, in ottica geometrica, aiutano a descrivere fenomeni di propagazione luminosa oltre le caus...

We study the existence and multiplicity of solutions for a class of coupled semilinear elliptic systems in R n where none of the potentials are coercive. The main goal is to consider systems where the...