ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: N 35 Dzhuraev, A., Tajik Academy of Sciences, Tajikistan On partial differential equations in the unit ball of ℂ^{n}, which are singular at the origin and on the boundary We are considering two kind of equations in the unit ball B of ℂ^{n}. First are second order equations

(R\overline{R} − |λ|^{2})u = 0

where

R\overline{R}u := ∑_{i,j=1}^{n} z_{i}\overline{z}_{j} \frac{∂^{2}u}{∂z_{i}\overline{z}_{j}}

and related first order equations

\overline{R}ω − λ\overline{ω} = 0 ,

where R is the radial operator and

\overline{R} :≡ ∑_{i=1}^{n} \overline{z}_{i} \frac{∂}{∂\overline{z}_{i}} .

Second kind of equations are the multidimensional overdetermined elliptic Beltrami systems, degenerated at the boundary of B.