Variational methods and PDEs
lecture room 408, 12:15 - 14:00
dr hab. Jarosław Mederski, prof. IM PAN
- January 21, 2019
- January 14, 2019
Jarosław Mederski (IM PAN):
General class of optimal Sobolev inequalities and nonlinear scalar field equations
Abstract: We find a class of optimal Sobolev inequalities with a general nonlinearity, and in particular we provide a new proof of the logarithmic Sobolev inequality. The optimizers of the inequalities satisfy nonlinear scalar field equations.
- November 5, 2018
Panayotis Smyrnelis (IM PAN):
Existence and properties of vortices in the Ginzburg-Landau model of liquid crystals
Abstract: In the theory of light-matter interaction in nematic liquid crystals, the vector field of the molecules is described by a singular problem involving a Ginzburg-Landau type system of PDE. I will establish the existence of vortices and discuss some of their properties.