ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 58, 30, 35 Egorov, Alexandre A., Sobolev Institute of Mathematics, Russia Stability of classes of Lipschitz-continuous solutions to systems of first-order linear partial differential equations Let 𝔇_{C} be the class of C-Lipschitz-continuous solutions g = (g_{1}, …, g_{m}) : U → ℝ^{m} (defined on domains U ⊂ ℝ^{n}) to the system

∑_{μ=1}^{m} ∑_{ν=1}^{n} a_{νμκ}∂_{ν}g_{μ}(x) = b_{κ}, κ = 1, …, k;  (1)

C ≥ 0, a_{νμκ}, b_{κ} ∈ ℝ. For any elliptic system (1) the class 𝔇_{C} is stable (in the sense of A. P. Kopylov’s ω-stability). Applications to studying ωstability for other classes will be presented. This research was financially supported by the RFBR (Grant 96–01–01769) and the Federal Program “Leading Scientific Schools” (Grant 96–15–96291). Reference: A. A. Egorov, Stability of classes of Lipschitz solutions of systems of first-order linear differential equations, Dokl. Akad. Nauk 356 (1997), 583–587.