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.
Notes on the Cauchy–Kowalevski Theorem for E-modules
✍ Scribed by Yuichi Sugiki; Kiyoshi Takeuchi
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 185 KB
- Volume
- 181
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
For a coherent E X -module M, Kashiwara and Schapira introduced the complex RHom EX (M, O X ) of holomorphic solutions to M. Very recently this complex was used by R. Ishimura (1998, J. Math. Pures Appl. 77, 647 654) to formulate and establish the Cauchy Kowalevski theorem for E-modules. In this paper, we will give a rigorous proof of some arguments of Ishimura.
📜 SIMILAR VOLUMES
The main aim of this note is to improve some results obtained in the author's earlier paper (1999, J. Math. Anal. Appl. 236, 350-369). From the improved result follow some useful criteria on the stochastic asymptotic stability and boundedness.
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