研究生短课程

时间: March 22 （Tues.） 1:00-4:00pm；March 24 （Thur.） 1:00-4:00pm；March 28 （Mon.） 3:00-5:00pm；March 31 （Thur.）1:00-3:30pm

摘要： In this series of lectures we will see how methods and results from the (linear) spectral theory of magnetic Schr"odinger operators can be applied to some problems in non-linear PDE. We will mainly consider the example of the optimal semi-classical magnetic Sobolev constants, but another important application would be the analysis of the Ginzburg-Landau model. We will review the needed technology from the concentration-compactness theory to prove existence of minimisers for model problems. Then we proceed to introduce adapted non-linear partitions of unity to derive the leading order of the magnetic Sobolev constants. Finally, we discuss how these results imply information on the localization of minimizers.