Vortrag "A Sobolev-type constant in the curl inequality and ground states for curl-curl problem with critical exponent"

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.