ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

1991 MS Classification: Pogorelenko, V., Voronezh University, Voronezh, Russia, and P. Sobolevskii, Hebrew University, Jerusalem, Israel The “counter-example” to W. Littman’s counter-example of L_{p}- energetical inequality for wave equation It is well known (W. Littman’s counter-example, 1963), that L_{p}-energetical inequality for solutions of multidimensional wave equation is true in the case p = 2 only. However there exists a multidimensional pseudodifferential elliptic operator of the second order such that for solutions of correspondent hyperbolic equation L_{p}-energetical inequality holds for any 1 < p < +∞. The proof of this statement is based on the boundedness in L_{p}-norm of some one dimensional pseudodifferential operator in the case, when Marcinkiewicz-Mikhlin’s theorem is not applicable.