Abstract
Abstract In this paper, we perform a refined blow-up analysis of finite energy approximated solutions to a Nirenberg-type problem on half spheres. The latter 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 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 nonsimple blow-up points for subcritical solutions having zero or nonzero weak limit. The formation of such nonsimple blowups is governed by a vortex problem, unveiling an unexpected connection with Euler equations in fluid dynamic and mean fields type equations in mathematical physics.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
