Concentration phenomena for singularly perturbed elliptic PDEs

09/07/2007 - 00:00
Andrea Malchiodi (ISAS, Trieste)
We consider a class of nonlinear elliptic equations with a singular perturbation parameter $\epsilon$, which arise from physical or biologial models, like the nonlinear Schroedinger equation or the Gierer-Meinhardt system. In the last twenty years, a lot of attention has been devoted to study the asymptotics of solutions, and more recently some results about concentration at sets of positive dimension have been derived. We discuss the recent progress in this direction and some open problems.
Last edited by on Mon, 08/27/2007 - 11:28