We show that the Neumann problem for Laplace's equation in a convex domain ω with boundary data in Lp(∂ω) is uniquely solvable for 1 < p < ∞. As a consequence, we obtain the Helmholtz decomposition of vector fields in Lp(ω,Rd).
|Number of pages||18|
|Journal||Journal of Functional Analysis|
|State||Published - Oct 2010|
Bibliographical noteFunding Information:
* Corresponding author. E-mail addresses: firstname.lastname@example.org (J. Geng), email@example.com (Z. Shen). 1 Supported in part by NSF grant DMS-0855294.
- Convex domains
- Helmholtz decomposition
- Neumann problem
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