Weighted Sobolev Spaces and Exterior Problems for the Helmholtz Equation
β Scribed by P. Neittaanmaki and G. F. Roach
- Book ID
- 124931543
- Publisher
- The Royal Society
- Year
- 1987
- Tongue
- English
- Weight
- 747 KB
- Volume
- 410
- Category
- Article
- ISSN
- 0962-8444
- DOI
- 10.2307/2398213
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π SIMILAR VOLUMES
## Communicated by M. Lachowicz Let f β L 2,-l (R 3 ), where We prove the decomposition f =-βu+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|ββ.
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, 3ΒΈN. The in#uence of some compatibility conditions on the behaviour at i