Dottorato in Matematica:

 

Presentazione Tesi di Dottorato: Fabrizio Morlando

27/11/2013 - 14:00
Aula seminari 311 Largo San L. Murialdo

"Perturbative and variational methods for a class of elliptic equations with critical growth of exponential-type."

Abstract: In this talk, we deal with a class of elliptic PDEs with critical growth of exponential-type. A typical example is represented by the so-called Liouville equation in a planar domain. This type of equations and qualitatively similar ones arise in a broad range of applications and they have attracted great attention over the last decades. Furthermore, if we consider a N-dimensional domain with N>2, in order to preserve the criticality of the problem, we have to replace the Laplacian with the polyharmonic operator for all even dimensions N or with the N-Laplacian. For these types of problems, we show how the presence of topology in the domain strongly implies existence of solutions.