# Seminario de ecuaciones diferenciales

#### Detalles de Evento

Título: Concentration phenomena for the fractional $$Q$$-curvature equation in dimension 3 and fractional Poisson formulas.
Impartida por: Azahara De la Torre.
Abstract: We study compactness properties of metrics of prescribed fractional $$Q$$-curvature of order $$3$$ in $$\mathbb{R}^3$$. We use an approach inspired from conformal geometry, regarding a metric on a subset of $$\mathbb{R}^3$$ as the restriction of a metric on $$\mathbb{R}^4_+$$ with vanishing fourth-order $$Q$$-curvature. In particular, in analogy with a $$4$$-dimensional result of Adimurthi, Robert and Struwe, we prove that a sequence of such metrics with uniformly bounded fractional $$Q$$-curvature can blow up on a large set (roughly, the zero set of the trace of a nonpositive biharmonic function $$\Phi$$ in $$\mathbb{R}^4_+$$), and we also construct examples of such behaviour. Towards this result, an intermediate step of independent interest is the construction of general Poisson-type representation formulas (also for higher dimension).

This is a work done in collaboration with María del Mar González, Ali Hyder and Luca Martinazzi.

5 de septiembre de 2019, 10:00, Seminario 1ª planta IEMath-GR