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Gabriele Mancini (Università La Sapienza di Roma)
Título: Local and non-local Liouville type equations in Euclidean spaces.
Abstract: In this talk, I will give an overview on some existence and classification results for solutions to high-order, local and non-local Liouville equations, under a finite volume condition. Such solutions correspond to constant Q-curvature metrics on the Euclidean space. In high dimension, I will describe the distinction between normal and non-normal solutions: the former have logarithmic behavior at infinity and correspond to a standard volume value, while the latter have polynomial decay. I will present some results obtained in collaboration with A. Hyder and L. Martinazzi concerning the existence of a radial normal solution with a prescribed singularity at the origin, and the existence of non-normal solutions having non-standard volume.
Begoña Barrios (Universidad de La Laguna)
Título: Equivalence of weak and viscosity solutions in fractional non-homogeneous problems.
Abstract: In this talk we establish the equivalence between the notions of weak and viscosity solutions for non-homogeneous equations whose main operator is the fractional p-Laplacian and the lower order term depends on x, u and D_s^p u, being the last one a type of fractional derivative. The results of the talk have been obtained in collaboration with M. Medina.
Zoom link: https://uniroma1.zoom.us/j/82530225222?pwd=SCtZTW5idWg5YkROcmhIem4wM3ZMdz09
Webpage: https://sites.google.com/view/pdesespanaitalia.