Date/heure
28 février 2023
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Pierre-Damien Thizy (Université Claude Bernard Lyon 1)
Catégorie d'évènement Séminaire Équations aux Derivées Partielles et Applications (Nancy)
Résumé
On a bounded domain of the Euclidean space $\mathbb{R}^{2m}$, $m>1$, Adimurthi, Robert and Struwe pointed out that, even assuming a volume bound $\int e^{2mu} dx \leq C$, some blow-up solutions for prescribed Q-curvature equations $(-\Delta)^m u= Q e^{2m u}$ without boundary conditions may blow-up not only at points, but also on the zero set of some nonpositive nontrivial polyharmonic function. This is in striking contrast with the two dimensional case ($m=1$). During this talk, starting from a work in progress with Ali Hyder and Luca Martinazzi, we will discuss the construction of such solutions which involves (possible generalizations of) the Walsh-Lebesgue theorem and some issues about elliptic problems with measure data.