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...
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...
We present sharp decay rates as time tends to infinity for solutions to wave equations in domains with infinite boundaries like infinite waveguides, as well as the global well-posedness and the asympt...
Si discutono due equazioni di evoluzione in dimensione uno ottenute come sistema gradiente di due funzionali non convessi, il funzionale di Perona-Malik e il funzionale a doppio pozzo. A causa della n...
Introdurremo un sistema di due equazioni ellittiche debolmente accoppiate, proveniente da alcuni modelli dell’ottica quantistica, contenente un parametro piccolo. Discuteremo dell’esistenza e di alcun...
I review the connection between semilinear elliptic equations and their numerical aproximation. In particular, I consider how a recent counterexample of Souplet extends to regions with corners, and th...
Based on Griffith’s criterion for crack growth, a method was proposed for determining crack paths by taking continuous-time limits of discrete-time variational problems. This has been successfully car...
We extende the resolution of the Yamabe conjecture to the Cauchy-Riemann manifolds and precisely the case left open by D. Jenson and J. Lee: the conformally flat case and the case n = 1, where 2n + 1 ...
