Mikhail S. Agranovich

Spectral Problems in Lipschitz Domains in Sobolev-Type Banach Spaces

abstract:
This paper contains a short presentation of author's results on spectral properties of main boundary value problems for strongly elliptic second-order systems in bounded Lipschitz domains. We consider the questions on the completeness of root functions, on the summability of Fourier series with respect to them and on their basis property in spaces $H^s_p$ with indices $s, p$ close to $\pm 1, 2$. The complete presentation will be published elsewhere.

Mathematics Subject Classification: 35J57, 35P05, 35P10

Key words and phrases: Strongly elliptic system, Lipschitz domain, spectral problem, discrete spectrum, completeness of root functions, Abel-Lidskii summability