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SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Mercoledì 29 Ottobre 2014 alle ore 15:00 in aula 2BC30, Daniele Bartolucci (Università di Roma Tor Vergata) terrà un seminario dal titolo "Supercritical Liouville-type systems".
We are concerned with solutions of elliptic systems of Liouville-type equations on simply connected domains. New necessary conditions for the existence of solutions are found which suggest that those systems can be solved in a supercritical region of parameters where the associated variational functional has no minimizers. In sharp contrast with other well known results, the existence of these solutions depends on the geometry of the domain rather than on its topology. Indeed, among other things, we will show that such solutions exist on any convex domain whose isoperimetric ratio is large enough.
Rif. Int. M. Bardi, C. Marchi, D. Castorina.