Seminari del Dipartimento


Analisi Matematica

Concentration phenomena for the fractional Q-curvature equation in dimension 3 and fractional Poisson formulas.

Azahara de la Torre

09-10-2019 - 15:00
Largo San Leonardo Murialdo,1 - Pal.C - Aula 311


We study compactness properties of metrics of prescribed fractional Q-curvature of order 3 in R^3. We use an approach inspired from conformal geometry, regarding a metric on a subset of R^3 as the restriction of a metric on 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 in 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 Maria del Mar Gonzalez, Ali Hyder and Luca Martinazzi.

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