New Blow up phenomena for the Nirenberg's problem on half spheres

Abstract: In this talk I will report on a refined blow up analysis of finite energy approximated solutions to the Nirenberg's problem on half spheres. The later consists of prescribing under minimal boundary conditions the scalar curvature to be a given function. In particular we give a precise location of blow up points and blow up rates. Such an analysis shows that the blow up picture of the Nirenberg's problem on half spheres is far more complicated that in the case of closed spheres. Indeed besides the combination of interior and boundary blow ups, there are "non simples blow ups" for subcritical solutions having zero or nonzero weak limit. The formation of such non simple blow ups is governed by a vortex problem, unveiling an unexpected connection with Euler equations in fluid dynamic and mean fields type equations in mathematical physics. This is joint work with Mohamed Ben Ayed (Sfax University).

differential geometryfunctional analysis

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php