I will present some results concerning the existence of nodal solutions to the Yamabe equation on the sphere and their connections with the existence of positive solutions to competitive elliptic syst...
In this joint work with Marc Briane I will revisit one of the most elementary homogenization problems ever and demonstrate that abandonment of just one assumption, very strong ellipticity, drastically...
In this talk we discuss some recent results about a class of fully nonlinear second order partial differential problems in nondivergence form, uniformly elliptic with quadratic growth in the gradient....
We provide a representation formula for viscosity solutions to a nonlinear second order parabolic PDE problem with sublinear operators. This is done through a dynamic programming principle which is a ...
In questo seminario presenterò alcuni dei risultati principali ottenuti nella mia tesi di dottorato. Essi riguardano alcune questioni relative a due classi di problemi di Dirichlet ellittici non coerc...
It is well known that cubic NLS is a completely integrable model and in particular there exist infinitely many conserved quantities associated with this equation. We shall discuss a possible approach ...
We consider an equation in divergence form with a singular/degenerate weight. We first study the regularity of the nodal sets of solutions in the linear case. Next, when the r.h.s. does not depend on ...
We prove, using variational methods, the existence in dimension two of positive vector ground states solutions for Bose-Einstein type systems. The nonlinear interaction between two Bose fluids is assu...
We study the behavior as t \to +\infty of unbounded solutions of the so-called viscous Hamilton-Jacobi equation in the whole space R^N, in the superquadratic case; i.e., u_t - \Delta u +...
The measure theoretic generalization of oriented submanifolds of R^N of any dimension, are currents. One the most important theorem is the compactness criterium of Federer-Fleming. We try to prove and...
