Vortrag "A Sobolev-type constant in the curl inequality and ground states for curl-curl problem with critical exponent"
Jaroslav Mederski
- https://www.uni-giessen.de/de/fbz/fb07/fachgebiete/mathematik/mathematik/kalender/2021/2021-04-29
- Vortrag "A Sobolev-type constant in the curl inequality and ground states for curl-curl problem with critical exponent"
- 2021-04-29T16:15:00+02:00
- 2021-04-29T17:15:00+02:00
- Jaroslav Mederski
29.04.2021 von 16:15 bis 17:15 (Europe/Berlin / UTC200)
MSTeams
Abstract
Sharp Sobolev-type inequalities have been widely studied by a large number of authors and the best Sobolev constants play an important role e.g. in mathematical physics.
Our aim is to perform a similar analysis for the curl operator defined on a bounded domain or in R^3. We propose a new optimal curl inequality, which provides ground state solutions to the semilinear curl-curl problem involving the critical Sobolev exponent. We present a concentration-compactness analysis for the curl-curl problem and we find solutions by means of variational methods for strongly indefinite functionals. This is a joint work with Andrzej Szulkin.