Speaker
Jarosław Mederski
(POLISH ACADEMY OF SCIENCES)
Description
(Jarosław Mederski - Polish Academy of Sciences)
Nonlinear curl-curl problems have recently emerged in the study of exact electromagnetic wave propagation in nonlinear media modeled by Maxwell's equations. For example, the quintic effect leads to a critical partial differential equation involving the curl-curl operator. Ground state solutions of this problem are related to the optimizers of a new Sobolev-type inequality. We present recent results concerning the existence of ground state solutions and discuss certain symmetry properties of the problem. Applications to zero modes of the Dirac equations will also be considered.
