## Communicated by M. Lachowicz Let f โ L 2,-l (R 3 ), where We prove the decomposition f =-โu+g, with g divergence free and u is a solution to the problem in R 3 Since f, u, g are defined in R 3 we need a sufficiently fast decay of these functions as |x|โโ.
The behavior of the laplacian on weighted sobolev spaces
โ Scribed by Robert C. McOwen
- Publisher
- John Wiley and Sons
- Year
- 1979
- Tongue
- English
- Weight
- 443 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0010-3640
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract The boundedness of the finite Hilbert transform operator on certain weighted __L~p~__ spaces is well known. We extend this result to give the boundedness of that operator on certain weighted Sobolev spaces. (ยฉ 2004 WILEYโVCH Verlag GmbH & Co. KGaA, Weinheim)
We extend here some existence and uniqueness results for the exterior Stokes problem in weighted Sobolev spaces. We also study the regularity of the solutions (u, ) and prove optimal a priori estimates for the solutions with u, 3ยธN. The in#uence of some compatibility conditions on the behaviour at i
## Abstract In this paper, we investigate the Stokes system and the biharmonic equation in a halfโspace of โ^__n__^. Our approach rests on the use of a family of weighted Sobolev spaces as a framework for describing the behaviour at infinity. A complete class of existence, uniqueness and regularity
## Abstract We investigate the composition operators on the weighted Hardy spaces __H__^2^(__ฮฒ__). For any bounded weight sequence __ฮฒ__, we give necessary conditions for those operators to be isometric. The sufficiency of those conditions is wellโknown for the classical space __H__^2^. In the case
We prove a general embedding theorem for Sobolev spaces on open manifolds of bounded geometry and infer from this the module structure theorem. Thereafter we apply this to weighted Sobolev spaces.