Speaker
Description
First we plan to discuss the Dirichlet problem for second order homogeneous elliptic equations with constant complex coefficients in domains in the complex plane. We will present and discuss the following result: every Jordan domain in $\mathbb C$ with $C^{1,\alpha}$-smooth boundary, $\alpha\in(0,1)$, is not regular with respect to the Dirichlet problem for any not strongly elliptic equation of the specified type. Next we will touch the problem on uniform approximation of functions on compact sets in the complex plane by polynomial solutions of such equations. We present some recent results and open questions concerning this problem and its links with the Dirichlet problems under consideration.
The talk is based on a joint work with A. Bagapsh and M. Mazalov
