Large blow-up sets for Q-curvature equations - Institut Élie Cartan de Lorraine

Date/heure
28 février 2023
10:45 - 11:45

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

R^{2 m}

m > 1

, Adimurthi, Robert and Struwe pointed out that, even assuming a volume bound

\int e^{2 m u} d x \leq C

, some blow-up solutions for prescribed Q-curvature equations

(- Δ)^{m} u = Q e^{2 m 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.